The mathematical study of voting, social choice theory , has traditionally only been applicable to choices among predetermined alternatives, but not to open-ended decisions such as collectively selecting a textual statement. We introduce generative social choice , a design methodology for open-ended democratic processes that combines the rigor of social choice theory with the capability of large language models to generate text and extrapolate preferences. Our framework divides the design of AI-augmented democratic processes into two components: first, proving that the process satisfies representation guarantees when given access to oracle queries; second, empirically validating that these queries can be approximately implemented using a large language model. We apply this framework to the problem of summarizing free-form opinions into a proportionally representative set of opinion statements; specifically, we develop a democratic process with representation guarantees and use this process to portray the opinions of participants in a survey about abortion policy. In a trial with 100 representative US residents, we find that 84 out of 100 participants feel “excellently” or “exceptionally” represented by the set of five statements we extracted.

Effective human-AI coordination requires artificial agents capable of exhibiting and responding to human-like behaviors while adapting to changing contexts. Imitation learning has emerged as one of the prominent approaches to build such agents by training them to mimic human-demonstrated behaviors. However, current methods struggle to capture the inherent diversity and non-Markovian nature of human behavior and lack the ability to steer behavior at inference time. Drawing inspiration from the theory of human cognitive processes, where inner speech guides action selection before execution, we propose MIMIC (Modeling Inner Motivations for Imitation and Control), a framework that uses language as an internal representation of behavioral intent. MIMIC employs the novel use of vision-language models as linguistic scaffolding to train a conditional variational autoencoder capable of generating inner speech from observations. A diffusion-based behavior cloning policy then selects actions conditioned on current observations and the generated inner speech. MIMIC enables fine-grained steering of behavior at inference time by conditioning the agent on behavior-specific speech. Experiments across robotic manipulation tasks and human-AI collaboration games demonstrate that MIMIC significantly enhances both behavior diversity and fidelity to human demonstrations while enabling nuanced behavioral steering without training on additional demonstrations.

Differentiable economics—the use of deep learning for auction design—has driven progress in multi-item auction design with additive and unit-demand valuations. However, there has been little progress for combinatorial auctions (CAs), even in the simplest and yet important single bidder case, due to exponential growth of the bundle space with the number of items. We address this challenge by introducing a deep network architecture for a menu-based CA, which supports the first dominant-strategy incentive compatible (DSIC), revenue-optimizing single-bidder CA. Our idea is to generate a bundle distribution through an ordinary differential equation (ODE) applied to a tractable initial distribution. The BundleFlow method learns suitable ODE-based transforms, one for each menu element, to optimize expected revenue. BundleFlow achieves up to 2.23$\times$ higher revenue than baselines on standard CA testbeds and scales up to 500 items. Compared with other menu-learning baselines, BundleFlow also reduces training iterations by 3.6-9.5$\times$ and cuts training time by about 80% in settings with 50 and 100 items.

We consider a platform in a two-sided market with unit-supply sellers and unit-demand buyers. Each buyer can transact with a subset of sellers it knows off platform and another seller that the platform recommends. Given the choice of sellers, transactions and prices form a competitive equilibrium. The platform selects one seller for each buyer, and charges a fixed percentage of prices to all transactions that it recommends. The platform seeks to maximize total revenue. We show that the platform's problem is NP-hard, even when each buyer knows at most two buyers off platform. Finally, when each buyer values all sellers equally and knows only one buyer off platform, we provide a polynomial time algorithm that optimally solves the problem.

We introduce the use of generative adversarial learning to compute equilibria in general game-theoretic settings, specifically the generalized Nash equilibrium (GNE) in pseudo-games, and its specific instantiation as the competitive equilibrium (CE) in Arrow-Debreu competitive economies. Pseudo-games are a generalization of games in which players' actions affect not only the payoffs of other players but also their feasible action spaces. Although the computation of GNE and CE is intractable in the worst-case, i.e., PPAD-hard, in practice, many applications only require solutions with high accuracy in expectation over a distribution of problem instances. We introduce Generative Adversarial Equilibrium Solvers (GAES): a family of generative adversarial neural networks that can learn GNE and CE from only a sample of problem instances. We provide computational and sample complexity bounds for Lipschitz-smooth function approximators in a large class of concave pseudo-games, and apply the framework to finding Nash equilibria in normal-form games, CE in Arrow-Debreu competitive economies, and GNE in an environmental economic model of the Kyoto mechanism.

Congestion is a common failure mode of markets, where consumers compete inefficiently on the same subset of goods (e.g., chasing the same small set of properties on a vacation rental platform). The typical economic story is that prices decongest by balancing supply and demand. But in modern online marketplaces, prices are typically set in a decentralized way by sellers, and the information about items is inevitably partial. The power of a platform is limited to controlling *representations*---the subset of information about items presented by default to users. This motivates the present study of *decongestion by representation*, where a platform seeks to learn representations that reduce congestion and thus improve social welfare. The technical challenge is twofold: relying only on revealed preferences from the choices of consumers, rather than true preferences; and the combinatorial problem associated with representations that determine the features to reveal in the default view. We tackle both challenges by proposing a *differentiable proxy of welfare* that can be trained end-to-end on consumer choice data. We develop sufficient conditions for when decongestion promotes welfare, and present the results of extensive experiments on both synthetic and real data that demonstrate the utility of our approach.

We consider *multiple senders* with informational advantage signaling to convince a single self-interested actor to take certain actions. Generalizing the seminal *Bayesian Persuasion* framework, such settings are ubiquitous in computational economics, multi-agent learning, and machine learning with multiple objectives. The core solution concept here is the Nash equilibrium of senders' signaling policies. Theoretically, we prove that finding an equilibrium in general is PPAD-Hard; in fact, even computing a sender's best response is NP-Hard. Given these intrinsic difficulties, we turn to finding local Nash equilibria. We propose a novel differentiable neural network to approximate this game's non-linear and discontinuous utilities. Complementing this with the extra-gradient algorithm, we discover local equilibria that Pareto dominates full-revelation equilibria and those found by existing neural networks. Broadly, our theoretical and empirical contributions are of interest to a large class of economic problems.

Artificial Intelligence (AI) holds promise as a technology that can be used to improve government and economic policy-making. This paper proposes a new research agenda towards this end by introducing Social Environment Design, a general framework for the use of AI in automated policy-making that connects with the Reinforcement Learning, EconCS, and Computational Social Choice communities. The framework seeks to capture general economic environments, includes voting on policy objectives, and gives a direction for the systematic analysis of government and economic policy through AI simulation. We highlight key open problems for future research in AI-based policymaking. By solving these challenges, we hope to achieve various social welfare objectives, thereby promoting more ethical and responsible decision making.

Differentiable economics uses deep learning for automated mechanism design. Despite strong progress, it has remained an open problem to learn multi-bidder, general, and fully strategy-proof (SP) auctions. We introduce GEneral Menu-based NETwork (GemNet), which significantly extends the menu-based approach of RochetNet [Dütting et al., 2024] to the multi-bidder setting. The challenge in achieving SP is to learn bidder-independent menus that are feasible, so that the optimal menu choices for each bidder do not over-allocate items when taken together (we call this menu compatibility). GemNet penalizes the failure of menu compatibility during training, and transforms learned menus after training through price changes, by considering a set of discretized bidder values and reasoning about Lipschitz smoothness to guarantee menu compatibility on the entire value space. This approach is general, leaving undisturbed trained menus that already satisfy menu compatibility and reducing to RochetNet for a single bidder. Mixed-integer linear programs are used for menu transforms and through a number of optimizations enabled by deep learning, including adaptive grids and methods to skip menu elements, we scale to large auction design problems. GemNet learns auctions with better revenue than affine maximization methods, achieves exact SP whereas previous general multi-bidder methods are approximately SP, and offers greatly enhanced interpretability. The full version of this paper is available at https://arxiv.org/abs/2406.07428.

We model the role of an online platform disrupting a market with unit-demand buyers and unit-supply sellers. Each seller can transact with a subset of the buyers whom she already knows, as well as with any additional buyers to whom she is introduced by the platform. Given these constraints on trade, prices and transactions are induced by a competitive equilibrium. The platform's revenue is proportional to the total price of all trades between platform-introduced buyers and sellers.

We introduce the theoretical study of a Platform Equilibrium in a market with unit-demand buyers and unit-supply sellers. Each seller can join a platform and transact with any buyer or remain off-platform and transact with a subset of buyers whom she knows. Given the constraints on trade, prices form a competitive equilibrium and clears the market. The platform charges a transaction fee to all on-platform sellers, in the form of a fraction of on-platform sellers' price. The platform chooses the fraction to maximize revenue. A Platform Equilibrium is a Nash equilibrium of the game where each seller decides whether or not to join the platform, balancing the effect of a larger pool of buyers to trade with, against the imposition of a transaction fee.

The mathematical study of voting, social choice theory, has traditionally only been applicable to choices among a few predetermined alternatives, but not to open-ended decisions such as collectively selecting a textual statement. We introduce generative social choice, a design methodology for open-ended democratic processes that combines the rigor of social choice theory with the capability of large language models to generate text and extrapolate preferences. Our framework divides the design of AI-augmented democratic processes into two components: first, proving that the process satisfies representation guarantees when given access to oracle queries; second, empirically validating that these queries can be approximately implemented using a large language model. We apply this framework to the problem of summarizing free-form opinions into a proportionally representative slate of opinion statements; specifically, we develop a democratic process with representation guarantees and use this process to represent the opinions of participants in a survey about chatbot personalization. In a trial with 100 representative US residents, we find that 93 out of 100 participants feel "mostly" or "perfectly" represented by the slate of five statements we extracted. By providing rigorous guarantees through social choice, our work alleviates concerns about AI-driven democratic innovation and helps unlock its potential.

Designing an incentive compatible auction that maximizes expected revenue is an intricate task. The single-item case was resolved in a seminal piece of work by Myerson in 1981, but more than 40 years later, a full analytical understanding of the optimal design still remains elusive for settings with two or more items. In this work, we initiate the exploration of the use of tools from deep learning for the automated design of optimal auctions. We model an auction as a multi-layer neural network, frame optimal auction design as a constrained learning problem, and show how it can be solved using standard machine learning pipelines. In addition to providing generalization bounds, we present extensive experimental results, recovering essentially all known solutions that come from the theoretical analysis of optimal auction design problems and obtaining novel mechanisms for settings in which the optimal mechanism is unknown.

Machine learning models are often used to inform real world risk assessment tasks: predicting consumer default risk, predicting whether a person suffers from a serious illness, or predicting a person's risk to appear in court. Given multiple models that perform almost equally well for a prediction task, to what extent do predictions vary across these models? If predictions are relatively consistent for similar models, then the standard approach of choosing the model that optimizes a penalized loss suffices. But what if predictions vary significantly for similar models? In machine learning, this is referred to as predictive multiplicity i.e. the prevalence of conflicting predictions assigned by near-optimal competing models. In this paper, we present a framework for measuring predictive multiplicity in probabilistic classification (predicting the probability of a positive outcome). We introduce measures that capture the variation in risk estimates over the set of competing models, and develop optimization-based methods to compute these measures efficiently and reliably for convex empirical risk minimization problems. We demonstrate the incidence and prevalence of predictive multiplicity in real-world tasks. Further, we provide insight into how predictive multiplicity arises by analyzing the relationship between predictive multiplicity and data set characteristics (outliers, separability, and majority-minority structure). Our results emphasize the need to report predictive multiplicity more widely.

Uniswap v3 is the largest decentralized exchange for digital currencies. A novelty of its design is that it allows a liquidity provider (LP) to allocate liquidity to one or more closed intervals of the price of an asset instead of the full range of possible prices. An LP earns fee rewards proportional to the amount of its liquidity allocation when prices move in this interval. This induces the problem of strategic liquidity provision: smaller intervals result in higher concentration of liquidity and correspondingly larger fees when the price remains in the interval, but with higher risk as prices may exit the interval leaving the LP with no fee rewards. Although reallocating liquidity to new intervals can mitigate this loss, it comes at a cost, as LPs must expend gas fees to do so. We formalize the dynamic liquidity provision problem and focus on a general class of strategies for which we provide a neural network-based optimization framework for maximizing LP earnings. We model a single LP that faces an exogenous sequence of price changes that arise from arbitrage and non-arbitrage trades in the decentralized exchange. We present experimental results informed by historical price data that demonstrate large improvements in LP earnings over existing allocation strategy baselines. Moreover we provide insight into qualitative differences in optimal LP behaviour in different economic environments.

AI methods are used in societally important settings, ranging from credit to employment to housing, and it is crucial to provide fairness in regard to automated decision making. Moreover, many settings are dynamic, with populations responding to sequential decision policies. We introduce the study of reinforcement learning (RL) with stepwise fairness constraints, which require group fairness at each time step. In the case of tabular episodic RL, we provide learning algorithms with strong theoretical guarantees in regard to policy optimality and fairness violations. Our framework provides tools to study the impact of fairness constraints in sequential settings and brings up new challenges in RL.

Stackelberg equilibria arise naturally in a range of popular learning problems, such as in security games or indirect mechanism design, and have received increasing attention in the reinforcement learning literature. We present a general framework for implementing Stackelberg equilibria search as a multi-agent RL problem, allowing a wide range of algorithmic design choices. We discuss how previous approaches can be seen as specific instantiations of this framework. As a key insight, we note that the design space allows for approaches not previously seen in the literature, for instance by leveraging multitask and meta-RL techniques for follower convergence. We propose one such approach using contextual policies, and evaluate it experimentally on both standard and novel benchmark domains, showing greatly improved sample efficiency compared to previous approaches. Finally, we explore the effect of adopting algorithm designs outside the borders of our framework.

Contract design involves a principal who establishes contractual agreements about payments for outcomes that arise from the actions of an agent. In this paper, we initiate the study of deep learning for the automated design of optimal contracts. We introduce a novel representation: the Discontinuous ReLU (DeLU) network, which models the principal's utility as a discontinuous piecewise affine function of the design of a contract where each piece corresponds to the agent taking a particular action. DeLU networks implicitly learn closed-form expressions for the incentive compatibility constraints of the agent and the utility maximization objective of the principal, and support parallel inference on each piece through linear programming or interior-point methods that solve for optimal contracts. We provide empirical results that demonstrate success in approximating the principal's utility function with a small number of training samples and scaling to find approximately optimal contracts on problems with a large number of actions and outcomes.

The _data market design_ problem is a problem in economic theory to find a set of signaling schemes (statistical experiments) to maximize expected revenue to the information seller, where each experiment reveals some of the information known to a seller and has a corresponding price. Each buyer has their own decision to make in a world environment, and their subjective expected value for the information associated with a particular experiment comes from the improvement in this decision and depends on their prior and value for different outcomes. In a setting with multiple buyers, a buyer's expected value for an experiment may also depend on the information sold to others. We introduce the application of deep learning for the design of revenue-optimal data markets, looking to expand the frontiers of what can be understood and achieved. Relative to earlier work on deep learning for auction design, we must learn signaling schemes rather than allocation rules and handle _obedience constraints_ — these arising from modeling the downstream actions of buyers — in addition to incentive constraints on bids. Our experiments demonstrate that this new deep learning framework can almost precisely replicate all known solutions from theory, expand to more complex settings, and be used to establish the optimality of new designs for data markets and make conjectures in regard to the structure of optimal designs.

Doctoral programs often have high rates of depression, anxiety, isolation, and imposter phenomenon. Consequently, graduating students may feel inadequately prepared for research-focused careers, contributing to an attrition of talent. Prior work identifies an important contributing factor to maladjustment: even with prior exposure to research, entering Ph.D. students often have problematically idealized views of science. These preconceptions can become obstacles for students in their own professional growth. Unfortunately, existing curricular and extracurricular programming in many doctoral programs fail to include mechanisms to systematically address students' misconceptions of their profession. In this work, we describe a new initiative at our institution that aims to address Ph.D. mental health via a mandatory seminar for entering doctoral students. The seminar is designed to build professional resilience in students by (1) increasing self-regulatory competence, and (2) teaching students to proactively examine academic cultural values and to participate in shaping them. Our evaluation indicates that students improved in both areas after completing the seminar.

Trading on decentralized exchanges has been one of the primary use cases for permissionless blockchains with daily trading volume exceeding billions of U.S. ‍dollars. In the status quo, users broadcast transactions they wish to execute in the exchange and miners are responsible for composing a block of transactions and picking an execution ordering — the order in which transactions execute in the exchange. Due to the lack of a regulatory framework, it is common to observe miners exploiting their privileged position by front-running transactions and obtaining risk-fee profits. Indeed, the Flashbots service institutionalizes this exploit, with miners auctioning the right to front-run transactions. In this work, we propose to modify the interaction between miners and users and initiate the study of verifiable sequencing rules. As in the status quo, miners can determine the content of a block; however, they commit to respecting a sequencing rule that constrains the execution ordering and is verifiable (there is a polynomial time algorithm that can verify if the execution ordering satisfies such constraints). Thus in the event a miner deviates from the sequencing rule, anyone can generate a proof of non-compliance.

We study the behavior of an economic platform (e.g., Amazon, Uber Eats, Instacart) under shocks, such as COVID-19 lockdowns, and the effect of different regulation considerations. To this end, we develop a multi-agent simulation environment of a platform economy in a multi-period setting where shocks may occur and disrupt the economy. Buyers and sellers are heterogeneous and modeled as economically-motivated agents, choosing whether or not to pay fees to access the platform. We use deep reinforcement learning to model the fee-setting and matching behavior of the platform, and consider two major types of regulation frameworks: (1) taxation policies and (2) platform fee restrictions. We offer a number of simulated experiments that cover different market settings and shed light on regulatory tradeoffs. Our results show that while many interventions are ineffective with a sophisticated platform actor, we identify a particular kind of regulation—fixing fees to the optimal, no-shock fees while still allowing a platform to choose how to match buyers and sellers—as holding promise for promoting the efficiency and resilience of the economic system.

Understanding the emerging behaviors of reinforcement learning agents may be difficult because such agents are often trained using highly complex and expressive models. In recent years, most approaches developed for explaining agent behaviors rely on domain knowledge or on an analysis of the agent’s learned policy. For some domains, relevant knowledge may not be available or may be insufficient for producing meaningful explanations. We suggest using formal model abstractions and transforms, previously used mainly for expediting the search for optimal policies, to automatically explain discrepancies that may arise between the behavior of an agent and the behavior that is anticipated by an observer. We formally define this problem of Reinforcement Learning Policy Explanation(RLPE), suggest a class of transforms which can be used for explaining emergent behaviors, and suggest meth-ods for searching efficiently for an explanation. We demonstrate the approach on standard benchmarks.

Algorithmic pricing on online e-commerce platforms raises the concern of tacit collusion, where reinforcement learning algorithms learn to set collusive prices in a decentralized manner and through nothing more than profit feedback. This raises the question as to whether collusive pricing can be prevented through the design of suitable "buy boxes," i.e., through the design of the rules that govern the elements of e-commerce sites that promote particular products and prices to consumers. In this paper, we demonstrate that reinforcement learning (RL) can also be used by platforms to learn buy box rules that are effective in preventing collusion by RL sellers. For this, we adopt the methodology of Stackelberg POMDPs, and demonstrate success in learning robust rules that continue to provide high consumer welfare together with sellers employing different behavior models or having out-of-distribution costs for goods.

Understanding emerging behaviors of reinforcement learning (RL) agents may be difficult since such agents are often trained in complex environments using highly complex decision making procedures. This has given rise to a variety of approaches to explainability in RL that aim to reconcile discrepancies that may arise between the behavior of an agent and the behavior that is anticipated by an observer. Most recent approaches have relied either on domain knowledge, that may not always be available, on an analysis of the agent’s policy, or on an analysis of specific elements of the underlying environment, typically modeled as a Markov Decision Process (MDP). Our key claim is that even if the underlying model is not fully known (e.g., the transition probabilities have not been accurately learned) or is not maintained by the agent (i.e., when using model-free methods), the model can nevertheless be exploited to automatically generate explanations. For this purpose, we suggest using formal MDP abstractions and transforms, previously used in the literature for expediting the search for optimal policies, to automatically produce explanations. Since such transforms are typically based on a symbolic representation of the environment, they can provide meaningful explanations for gaps between the anticipated and actual agent behavior. We formally define the explainability problem, suggest a class of transforms that can be used for explaining emergent behaviors, and suggest methods that enable efficient search for an explanation. We demonstrate the approach on a set of standard benchmarks.

A long line of work in social psychology has studied variations in people’s susceptibility to persuasion—the extent to which they are willing to modify their opinions on a topic. This body of literature suggests an interesting perspective on theoretical models of opinion formation by interacting parties in a network: in addition to considering interventions that directly modify people’s intrinsic opinions, it is also natural to consider interventions that modify people’s susceptibility to persuasion. In this work, motivated by this fact, we propose an influence optimization problem. Specifically, we adopt a popular model for social opinion dynamics, where each agent has some fixed innate opinion, and a resistance that measures the importance it places on its innate opinion; agents influence one another’s opinions through an iterative process. Under certain conditions, this iterative process converges to some equilibrium opinion vector. For the unbudgeted variant of the problem, the goal is to modify the resistance of any number of agents (within some given range) such that the sum of the equilibrium opinions is minimized; for the budgeted variant, in addition the algorithm is given upfront a restriction on the number of agents whose resistance may be modified. We prove that the objective function is in general non-convex. Hence, formulating the problem as a convex program as in an early version of this work (Abebe et al., KDD’18) might have potential correctness issues. We instead analyze the structure of the objective function, and show that any local optimum is also a global optimum, which is somehow surprising as the objective function might not be convex. Furthermore, we combine the iterative process and the local search paradigm to design very efficient algorithms that can solve the unbudgeted variant of the problem optimally on large-scale graphs containing millions of nodes. Finally, we propose and evaluate experimentally a family of heuristics for the budgeted variant of the problem.

We introduce the use of reinforcement learning for indirect mechanisms, working with the existing class of sequential price mechanisms, which generalizes both serial dictatorship and posted price mechanisms and essentially characterizes all strongly obviously strategyproof mechanisms. Learning an optimal mechanism within this class forms a partially-observable Markov decision process. We provide rigorous conditions for when this class of mechanisms is more powerful than simpler static mechanisms, for sufficiency or insufficiency of observation statistics for learning, and for the necessity of complex (deep) policies. We show that our approach can learn optimal or near-optimal mechanisms in several experimental settings.

In recent years, prominent blockchain systems such as Bitcoin and Ethereum have experienced explosive growth in transaction volume, leading to frequent surges in demand for limited block space and causing transaction fees to fluctuate by orders of magnitude. The status quo auctions sell space using a first-price auction [27]; however, users find it difficult to estimate how much they need to bid in order to get their transactions accepted onto the chain. If they bid too low, their transactions can have long confirmation times. If they bid too high, they pay larger fees than necessary.

When machine predictors can achieve higher performance than the human decision-makers they support, improving the performance of human decision-makers is often conflated with improving machine accuracy. Here we propose a framework to directly support human decision-making, in which the role of machines is to reframe problems rather than to prescribe actions through prediction. Inspired by the success of representation learning in improving performance of machine predictors, our framework learns human-facing representations optimized for human performance. This “Mind Composed with Machine” framework incorporates a human decision-making model directly into the representation learning paradigm and is trained with a novel human-in-the-loop training procedure. We empirically demonstrate the successful application of the framework to various tasks and representational forms.

We extend goal recognition design to account for partially informed agents. In particular, we consider a two-agent setting in which one agent, the actor, seeks to achieve a goal but has only incomplete information about the environment. The second agent, the recognizer, has perfect information and aims to recognize the actor's goal from its behavior as quickly as possible. As a one-time offline intervention and with the objective of facilitating the recognition task, the recognizer can selectively reveal information to the actor. The problem of selecting which information to reveal, which we call information shaping, is challenging not only because the space of information shaping options may be large, but also because more information revelation need not make it easier to recognize an agent's goal. We formally define this problem, and suggest a pruning approach for efficiently searching the search space. We demonstrate the effectiveness and efficiency of the suggested method on standard benchmarks.

In human forecasting, proper scoring rules are used to elicit effort in providing accurate probability forecasts of future events.A challenge, though, is that users do not receive feedback about their forecasts until the outcomes are realized.Nor is it clear whether these schemes are effective in motivating continual attention, and updating forecasts on difficult or dynamically changing problems, for which there is a continuous inflow of new information over time.Through a large-scale experiment on Amazon Mechanical Turk (MTurk), we investigate whether peer prediction methods can be used to complement methods of proper scoring rules, and improve engagement of users and ultimately the quality of forecasts.Peer prediction provides immediate feedback, by comparing one forecaster's prediction with that of another, this feedback provided as rank placement or through incentive payments.One of a very small number of experimental studies into peer prediction, ours is the first to test peer prediction in this hybrid role.We show that providing daily feedback through peer prediction has a significant effect in increasing engagement with the forecasting platform.Moreover, a hybrid scheme that combines scoring rules with peer prediction feedback (via rank feedback) is, together with the basic scoring rule method, generally the best for accuracy.Since the hybrid scheme also improves user engagement, this suggests that the hybrid scheme would provide the best accuracy for longer term forecasting events.

Blockchains are intended to be immutable, so an attacker who is able to delete transactions through a chain reorganization (a malicious reorg) can perform a profitable double-spend attack. We study the rate at which an attacker can execute reorgs in the Tezos Proof-of-Stake protocol. As an example, an attacker with 40% of the staking power is able to execute a 20-block malicious reorg at an average rate of once per day, and the attack probability increases super-linearly as the staking power grows beyond 40%. Moreover, an attacker of the Tezos protocol knows in advance when an attack opportunity will arise, and can use this knowledge to arrange transactions to double-spend. We show that in particular cases, the Tezos protocol can be adjusted to protect against deep reorgs. For instance, we demonstrate protocol parameters that reduce the rate of length-20 reorg opportunities for a 40% attacker by two orders of magnitude. We also observe a trade-off between optimizing for robustness to deep reorgs (costly deviations that may be net profitable because they enable double-spends) and robustness to selfish mining (mining deviations that result in typically short reorgs that are profitable even without double-spends). That is, the parameters that optimally protect against one make the other attack easy. Finally, we develop a method that monitors the Tezos blockchain health with respect to malicious reorgs using only publicly available information.

Motivated by economic applications such as recommender systems, we study the behavior of stochastic bandits algorithms under \emph{strategic behavior} conducted by rational actors, i.e., the arms. Each arm is a \emph{self-interested} strategic player who can modify its own reward whenever pulled, subject to a cross-period budget constraint, in order to maximize its own expected number of times of being pulled. We analyze the robustness of three popular bandit algorithms: UCB, $\varepsilon$-Greedy, and Thompson Sampling. We prove that all three algorithms achieve a regret upper bound $\mathcal{O}(\max \{ B, K\ln T\})$ where $B$ is the total budget across arms, $K$ is the total number of arms and $T$ is the running time of the algorithms. This regret guarantee holds for \emph{arbitrary adaptive} manipulation strategy of arms. Our second set of main results shows that this regret bound is \emph{tight}— in fact, for UCB, it is tight even when we restrict the arms’ manipulation strategies to form a \emph{Nash equilibrium}. We do so by characterizing the Nash equilibrium of the game induced by arms’ strategic manipulations and show a regret lower bound of $\Omega(\max \{ B, K\ln T\})$ at the equilibrium.

A common approach to planning with partial information is replanning: compute a plan based on assumptions about unknown information and replan if these assumptions are refuted during execution. To date, most planners with incomplete information have been designed to provide guarantees on completeness and soundness for the generated plans. Switching focus to performance, we measure the robustness of a plan, which quantifies the plan’s ability to avoid failure. Given a plan and an agent’s belief, which describes the set of states it deems as possible, robustness counts the number of world states in the belief from which the plan will achieve the goal without the need to replan. We formally describe the trade-off between robustness and plan cost and offer a solver that is guaranteed to produce plans that satisfy a required level of robustness. By evaluating our approach on a set of standard benchmarks, we demonstrate how it can improve the performance of a partially informed agent.

Machine learning is a powerful tool for predicting human-related outcomes, from creditworthiness to heart attack risks. But when deployed transparently, learned models also affect how users act in order to improve outcomes. The standard approach to learning predictive models is agnostic to induced user actions and provides no guarantees as to the effect of actions. We provide a framework for learning predictors that are accurate, while also considering interactions between the learned model and user decisions. For this, we introduce look-ahead regularization which, by anticipating user actions, encourages predictive models to also induce actions that improve outcomes. This regularization carefully tailors the uncertainty estimates that govern confidence in this improvement to the distribution of model-induced actions. We report the results of experiments on real and synthetic data that show the effectiveness of this approach.

Recent work in the domain of misinformation detection has leveraged rich signals in the text and user identities associated with content on social media. But text can be strategically manipulated and accounts reopened under different aliases, suggesting that these approaches are inherently brittle. In this work, we investigate an alternative modality that is naturally robust: the pattern in which information propagates. Can the veracity of an unverified rumor spreading online be discerned solely on the basis of its pattern of diffusion through the social network?

An important question in a software economy is how to incentivize deep rather than shallow fixes. A deep fix corrects the root cause of a bug instead of suppressing the symptoms. This paper initiates the study of the problem of incentive design for open workflows in fixing code. We model the dynamics of the software ecosystem and introduce subsumption mechanisms. These mechanisms only make use of externally observable information in determining payments and promote competition between workers. We use a mean field equilibrium methodology to evaluate the performance of these mechanisms, demonstrating in simulation that subsumption mechanisms perform robustly across various environment configurations and satisfy important criteria for market design.

We consider the problem of how decision making can be fair when the underlying probabilistic model of the world is not known with certainty. We argue that recent notions of fairness in machine learning need to explicitly incorporate parameter uncertainty, hence we introduce the notion of Bayesian fairness as a suitable candidate for fair decision rules. Using balance, a definition of fairness introduced in (Kleinberg, Mullainathan, and Raghavan 2016), we show how a Bayesian perspective can lead to well-performing and fair decision rules even under high uncertainty.

What is the best way to define algorithmic fairness? While many definitions of fairness have been proposed in the computer science literature, there is no clear agreement over a particular definition. In this work, we investigate ordinary people's perceptions of three of these fairness definitions. Across two online experiments, we test which definitions people perceive to be the fairest in the context of loan decisions, and whether fairness perceptions change with the addition of sensitive information (i.e., race of the loan applicants). Overall, one definition (calibrated fairness) tends to be more pre- ferred than the others, and the results also provide support for the principle of affirmative action.

Designing an incentive compatible auction that maximizes expected revenue is an intricate task. The single-item case was resolved in a seminal piece of work by Myerson in 1981. Even after 30-40 years of intense research the problem remains unsolved for seemingly simple multi-bidder, multi-item settings. In this work, we initiate the exploration of the use of tools from deep learning for the automated design of optimal auctions. We model an auction as a multi-layer neural network, frame optimal auction design as a constrained learning problem, and show how it can be solved using standard pipelines. We prove generalization bounds and present extensive experiments, recovering essentially all known analytical solutions for multi-item settings, and obtaining novel mechanisms for settings in which the optimal mechanism is unknown.

We consider a two-agent MDP framework where agents repeatedly solve a task in a collaborative setting. We study the problem of designing a learning algorithm for the first agent (A1) that facilitates a successful collaboration even in cases when the second agent (A2) is adapting its policy in an unknown way. The key challenge in our setting is that the first agent faces non-stationarity in rewards and transitions because of the adaptive behavior of the second agent. We design novel online learning algorithms for agent A1 whose regret decays as $O(T^{1-\frac{3}{7} \cdot \alpha})$ with $T$ learning episodes provided that the magnitude of agent A2’s policy changes between any two consecutive episodes are upper bounded by $O(T^{-\alpha})$. Here, the parameter $\alpha$ is assumed to be strictly greater than $0$, and we show that this assumption is necessary provided that the learning parity with noise problem is computationally hard. We show that sub-linear regret of agent A1 further implies near-optimality of the agents’ joint return for MDPs that manifest the properties of a smooth game.

In domains such as medicine, it can be acceptable for machine learning models to include sensitive attributes such as gender and ethnicity. In this work, we argue that when there is this kind of treatment disparity, then it should be in the best interest of each group. Drawing on ethical principles such as beneficence ("do the best") and non-maleficence ("do no harm"), we show how to use sensitive attributes to train decoupled classifiers that satisfy preference guarantees. These guarantees ensure the majority of individuals in each group prefer their assigned classifier to (i) a pooled model that ignores group membership (rationality), and (ii) the model assigned to any other group (envy-freeness). We introduce a recursive procedure that adaptively selects group attributes for decoupling, and present formal conditions to ensure preference guarantees in terms of generalization error. We validate the effectiveness of the procedure on real-world datasets, showing that it improves accuracy without violating preference guarantees on test data.

We study revenue-optimal pricing and driver compensation in ridesharing platforms when drivers have heterogeneous preferences over locations. If a platform ignores drivers' location preferences, it may make inefficient trip dispatches; moreover, drivers may strategize so as to route towards their preferred locations. In a model with stationary and continuous demand and supply, we present a mechanism that incentivizes drivers to both (i) report their location preferences truthfully and (ii) always provide service. In settings with unconstrained driver supply or symmetric demand patterns, our mechanism achieves (full-information) first-best revenue. Under supply constraints and unbalanced demand, we show via simulation that our mechanism improves over existing mechanisms and has performance close to the first-best.

Recent breakthroughs in AI for multi-agent games like Go, Poker, and Dota, have seen great strides in recent years. Yet none of these games address the real-life challenge of cooperation in the presence of unknown and uncertain teammates. This challenge is a key game mechanism in hidden role games. Here we develop the DeepRole algorithm, a multi-agent reinforcement learning agent that we test on "The Resistance: Avalon", the most popular hidden role game. DeepRole combines counterfactual regret minimization (CFR) with deep value networks trained through self-play. Our algorithm integrates deductive reasoning into vector-form CFR to reason about joint beliefs and deduce partially observable actions. We augment deep value networks with constraints that yield interpretable representations of win probabilities. These innovations enable DeepRole to scale to the full Avalon game. Empirical game-theoretic methods show that DeepRole outperforms other hand-crafted and learned agents in five-player Avalon. DeepRole played with and against human players on the web in hybrid human-agent teams. We find that DeepRole outperforms human players as both a cooperator and a competitor.

Moulin [1980] characterizes the single-facility, deterministic strategy-proof mechanisms for social choice with single-peaked preferences as the set of generalized median rules. In contrast, we have only a limited understanding of multi-facility strategy-proof mechanisms, and recent work has shown negative worst case results for social cost. Our goal is to design strategy-proof, multi-facility mechanisms that minimize expected social cost. We first give a PAC learnability result for the class of multi-facility generalized median rules, and utilize neural networks to learn mechanisms from this class. Even in the absence of characterization results, we develop a computational procedure for learning almost strategy-proof mechanisms that are as good as or better than benchmarks from the literature, such as the best percentile and dictatorial rules.

A long line of work in social psychology has studied variations in people's susceptibility to persuasion -- the extent to which they are willing to modify their opinions on a topic. This body of literature suggests an interesting perspective on theoretical models of opinion formation on social networks: in addition to considering interventions that directly modify people's intrinsic opinions, it is also natural to consider those that modify people's susceptibility to persuasion. Here, we adopt a popular model for social opinion dynamics, and formalize the opinion maximization and minimization problems where interventions happen at the level of susceptibility. We show that modeling interventions at the level of susceptibility leads to an interesting family of new questions in network opinion dynamics. We find that the questions are quite different depending on whether there is an overall budget constraining the number of agents we can target or not. We give a polynomial-time algorithm for finding the optimal target-set to optimize the sum of opinions when there are no budget constraints on the size of the target-set. We show that this problem is NP-hard when there is a budget, and that the objective function is neither submodular nor supermodular. Finally, we propose a heuristic for the budgeted opinion optimization problem and show its efficacy at finding target-sets that optimize the sum of opinions on real world networks, including a Twitter network with real opinion estimates.

Cluster-based randomized experiments are popular designs for mitigating the bias of standard estimators when interference is present and classical causal inference and experimental design assumptions (such as SUTVA or ITR) do not hold. Without an exact knowledge of the interference structure, it can be challenging to understand which partitioning of the experimental units is optimal to minimize the estimation bias. In the paper, we introduce a monotonicity condition under which a novel two-stage experimental design allows us to determine which of two cluster-based designs yields the least biased estimator. We then consider the setting of online advertising auctions and show that reserve price experiments satisfy the monotonicity condition and the proposed framework and methodology apply. We validate our findings on an advertising auction dataset.

Without monetary payments, the Gibbard-Satterthwaite theorem proves that under mild requirements all truthful social choice mechanisms must be dictatorships. When payments are allowed, the Vickrey-Clarke-Groves (VCG) mechanism implements the value-maximizing choice, and has many other good properties: it is strategy-proof, onto, deterministic, individually rational, and does not not make positive transfers to the agents. By Roberts' theorem, with three or more alternatives, the weighted VCG mechanisms are essentially unique for domains with quasi-linear utilities. The goal of this paper is to characterize domains of non-quasi-linear utilities where "reasonable'' mechanisms (with VCG-like properties) exist. Our main result is a tight characterization of the maximal non quasi-linear utility domain, which we call the largest parallel domain. We extend Roberts' theorem to parallel domains, and use the generalized theorem to prove two impossibility results. First, any reasonable mechanism must be dictatorial when the type domain is quasi-linear together with any single non-parallel type. Second, for richer utility domains that still differ very slightly from quasi-linearity, every strategy-proof, onto and deterministic mechanism must be a dictatorship.

There is increasing interest in promoting participatory democracy, in particular by allowing voting by mail or internet and through random-sample elections. A pernicious concern, though, is that of vote buying, which occurs when a bad actor seeks to buy ballots, paying someone to vote against their own intent. This becomes possible whenever a voter is able to sell evidence of which way she voted. We show how to thwart vote buying through decoy ballots, which are not counted but are indistinguishable from real ballots to a buyer. We show that an Election Authority can significantly reduce the power of vote buying through a small number of optimally distributed decoys, and model societal processes by which decoys could be distributed.

We consider a two-player sequential game in which agents have the same reward function but may disagree on the transition probabilities of an underlying Markovian model of the world. By committing to play a specific policy, the agent with the correct model can steer the behavior of the other agent, and seek to improve utility. We model this setting as a multi-view decision process, which we use to formally analyze the positive effect of steering policies. Furthermore, we develop an algorithm for computing the agents' achievable joint policy, and we experimentally show that it can lead to a large utility increase when the agents' models diverge.

Peer prediction mechanisms incentivize agents to truthfully report their signals, in the absence of a verification mechanism, by comparing their reports with those of their peers. Prior work in this area is essentially restricted to the case of homogeneous agents, whose signal distributions are identical. This is limiting in many domains, where we would expect agents to differ in taste, judgment and reliability. Although the Correlated Agreement (CA) mechanism [30] can be extended to handle heterogeneous agents, the new challenge is with the efficient estimation of agent signal types. We solve this problem by clustering agents based on their reporting behavior, proposing a mechanism that works with clusters of agents and designing algorithms that learn such a clustering. In this way, we also connect peer prediction with the Dawid and Skene [5] literature on latent types. We retain the robustness against coordinated misreports of the CA mechanism, achieving an approximate incentive guarantee of ε-informed truthfulness. We show on real data that this incentive approximation is reasonable in practice, and even with a small number of clusters.

We provide an empirical analysis of peer prediction mechanisms, which reward participants for information in settings when there is no ground truth against which to score reports. We simulate the mechanisms on a dataset of three million peer assessments from the edX MOOC platform. We evaluate different mechanisms on score variability, which is connected to fairness, risk aversion, and participant learning. We also assess the magnitude of the incentives to invest effort, and study the effect of participant coordination on low-information signals. We find that the correlated agreement mechanism has lower variation in reward than other mechanisms. A concern is that the gain from exerting effort is relatively low across all mechanisms, due to frequent disagreement between peers. Our conclusions are relevant for crowdsourcing in education as well as other domains.

Planned experiments are the gold standard in reliably comparing the causal effect of switching from a baseline policy to a new policy. % One critical shortcoming of classical experimental methods, however, is that they typically do not take into account the dynamic nature of response to policy changes. For instance, in an experiment where we seek to understand the effects of a new ad pricing policy on auction revenue, agents may adapt their bidding in response to the experimental pricing changes. Thus, causal effects of the new pricing policy after such adaptation period, the {\em long-term causal effects}, are not captured by the classical methodology even though they clearly are more indicative of the value of the new policy. % Here, we formalize a framework to define and estimate long-term causal effects of policy changes in multiagent economies. Central to our approach is behavioral game theory, which we leverage to formulate the ignorability assumptions that are necessary for causal inference. Under such assumptions we estimate long-term causal effects through a latent space approach, where a behavioral model of how agents act conditional on their latent behaviors is combined with a temporal model of how behaviors evolve over time.

We exhibit a property of the VCG mechanism that can help explain the surprising rarity with which it is used even in settings with unit demand: a relative lack of robustness to inaccuracies in the choice of its parameters. For a standard position auction environment in which the auctioneer may not know the precise relative values of the positions, we show that under both complete and incomplete information a non-truthful mechanism supports the truthful outcome of the VCG mechanism for a wider range of these values than the VCG mechanism itself. The result for complete information concerns the generalized second-price mechanism and lends additional theoretical support to the use of this mechanism in practice. Particularly interesting from a technical perspective is the case of incomplete information, where a surprising combinatorial equivalence helps us to avoid confrontation with an unwieldy differential equation.

The problem of peer prediction is to elicit information from agents in settings without any objective ground truth against which to score reports. Peer prediction mechanisms seek to exploit correlations between signals to align incentives with truthful reports. A long-standing concern has been the possibility of uninformative equilibria. For binary signals, a multi-task mechanism achieves strong truthfulness, so that the truthful equilibrium strictly maximizes payoff. We characterize conditions on the signal distribution for which this mechanism remains strongly-truthful with non-binary signals, also providing a greatly simplified proof. We introduce the Correlated Agreement (CA) mechanism, which handles multiple signals and provides informed truthfulness: no strategy profile provides more payoff in equilibrium than truthful reporting, and the truthful equilibrium is strictly better than any uninformed strategy (where an agent avoids the effort of obtaining a signal). The CA mechanism is maximally strongly truthful, in that no mechanism in a broad class of mechanisms is strongly truthful on a larger family of signal distributions. We also give a detail-free version of the mechanism that removes any knowledge requirements on the part of the designer, using reports on many tasks to learn statistics while retaining epsilon-informed truthfulness.

We put forward a new model of congestion games where agents have uncertainty over the routes used by other agents. We take a non-probabilistic approach, assuming that each agent knows that the number of agents using an edge is within a certain range. Given this uncertainty, we model agents who either minimize their worst-case cost (WCC) or their worst-case regret (WCR), and study implications on equilibrium existence, convergence through adaptive play, and efficiency. Under the WCC behavior the game reduces to a modified congestion game, and welfare improves when agents have moderate uncertainty. Under WCR behavior the game is not, in general, a congestion game, but we show convergence and efficiency bounds for a simple class of games.

Finding a common time slot for a group event is a daily conundrum and illustrates key features of group decision-making. It is a complex interplay of individual incentives and group dynamics. A participant would like the final time to be convenient for her, but she is also expected to be cooperative towards other people's preferences. We combine large-scale data analysis with theoretical models from the voting literature to investigate strategic behaviors in event scheduling. We analyze all Doodle polls created in the US from July-September 2011 (over 340,000 polls), consisting of both hidden polls (a user cannot see other responses) and open polls (a user can see all previous responses). By analyzing the differences in behavior in hidden and open polls, we gain unique insights into strategies that people apply in a natural decision-making setting. Responders in open polls are more likely to approve slots that are very popular or very unpopular, but not intermediate slots. We show that this behavior is inconsistent with models that have been proposed in the voting literature, and propose a new model based on combining personal and social utilities to explain the data.

We establish PAC learnability of influence functions for three common influence models, namely, the Linear Threshold (LT), Independent Cascade (IC) and Voter models, and present concrete sample complexity results in each case. Our results for the LT model are based on interesting connections with neural networks; those for the IC model are based an interpretation of the influence function as an expectation over random draw of a subgraph and use covering number arguments; and those for the Voter model are based on a reduction to linear regression. We show these results for the case in which the cascades are only partially observed and we do not see the time steps in which a node has been influenced. We also provide efficient polynomial time learning algorithms for a setting with full observation, i.e. where the cascades also contain the time steps in which nodes are influenced.

We consider the design of experiments to evaluate treatments that are administered by self-interested agents, each seeking to achieve the highest evaluation and win the experiment. For example, in an advertising experiment, a company wishes to evaluate two marketing agents in terms of their efficacy in viral marketing, and assign a contract to the winner agent. Contrary to traditional experimental design, this problem has two new implications. First, the experiment induces a game among agents, where each agent can select from multiple versions of the treatment it administers. Second, the action of one agent -- selection of treatment version -- may affect the actions of another agent, with the resulting strategic interference complicating the evaluation of agents. An incentive-compatible experiment design is one with an equilibrium where each agent selects its natural action, which is the action that maximizes the performance of the agent without competition (e.g., expected number of conversions if agent is assigned the advertising contract).

Rank breaking is a methodology introduced by Azari Soufiani et al. (2013a) for applying a Generalized Method of Moments (GMM) algorithm to the estimation of parametric ranking models. Breaking takes full rankings and breaks, or splits them up, into counts for pairs of alternatives that occur in particular positions (e.g., first place and second place, second place and third place). GMMs are of interest because they can achieve significant speed-up relative to maximum likelihood approaches and comparable statistical efficiency. We characterize the breakings for which the estimator is consistent for random utility models (RUMs) including Plackett-Luce and Normal-RUM, develop a general sufficient condition for a full breaking to be the only consistent breaking, and provide a trichotomy theorem in regard to single-edge breakings. Experimental results are presented to show the computational efficiency along with statistical performance of the proposed method.

We design a protocol for dynamic prioritization of data on shared routers such as untethered 3G/4G devices. The mechanism prioritizes bandwidth in favor of users with the highest value, and is incentive compatible, so that users can simply report their true values for network access. A revenue pooling mechanism also aligns incentives for sellers, so that they will choose to use prioritization methods that retain the incentive properties on the buy-side. In this way, the design allows for an open architecture. In addition to revenue pooling, the technical contribution is to identify a class of stochastic demand models and a prioritization scheme that provides allocation monotonicity. Simulation results confirm efficiency gains from dynamic prioritization relative to prior methods, as well as the effectiveness of revenue pooling.

It is desirable for an economic mechanism that its properties hold in a robust way across multiple equilibria and under varying assumptions regarding the information available to the participants. In this paper we focus on the design of position auctions and seek mechanisms that guarantee high revenue in every efficient equilibrium under both complete and incomplete information. Our main result identifies a generalized first-price auction with multi-dimensional bids as the only standard design capable of achieving this goal, even though valuations are one-dimensional. The fact that expressiveness beyond the valuation space is necessary for robustness provides an interesting counterpoint to previous work, which has highlighted the benefits of simple bid spaces. From a technical perspective, our results are interesting because they establish equilibrium existence for a multi-dimensional bid space, where standard techniques for establishing equilibrium existence break down.

Wireless spectrum is a scare resource, but in practice much of it is underused by current owners. To enable better use of this spectrum, we propose an auction approach that leverages dynamic spectrum access techniques to allocate spectrum in a secondary market. These are markets where spectrum owners can either sell or lease spectrum to other parties. Unlike previous auction approaches, we seek to take advantage of the ability to share spectrum among some bidders while respecting the needs of others for exclusive use. Thus, unlike unlicensed spectrum (e.g., Wi-Fi), which can be shared by any device, and exclusive-use licensed spectrum, where sharing is precluded, we enable efficient allocation by supporting sharing alongside quality-of-service protections. We present SATYA (Sanskrit for "truth"), a strategyproof and scalable spectrum auction algorithm whose primary contribution is in the allocation of a right to contend for spectrum to both sharers and exclusive-use bidders. Achieving strategyproofness in our setting requires appropriate handling of the externalities created by sharing. Using realistic Longley-Rice-based propagation modeling and data from the FCC's CDBS database, we conduct extensive simulations that demonstrate SATYA's ability to handle heterogeneous agent types involving different transmit powers and spectrum needs.

Today’s communication networks and networked systems are highly complex and heterogeneous \nand are often owned by profit-making entities. For new technologies or \ninfrastructure designs to be adopted, they must not only be based on sound engineering \nperformance considerations but also present the right economic incentives. Recent \nchanges in regulations of the telecommunication industry make such economic considerations \neven more urgent. For instance, new concerns such as network neutrality \nhave a significant impact on the evolution of communication networks. \nAt the same time, communication networks and networked systems support increasing \neconomic activity based on applications and services such as cloud computing, \nsocial networks, and peer-to-peer networks. These applications pose new challenges \nincluding the development of good pricing and incentive mechanisms to promote effective \nsystem-wide behavior. Similarly, the security and privacy of these applications are \nthemselves heavily dependent on economic considerations, which therefore need to be \nfully understood. \nTo address these questions, this special issue brings together a relevant set of state-of-the-art research contributions on complementary topics including communication \nnetworks, wireless networks, web content and security, and the use of multidisciplinary \napproaches ranging from game theory and economic modeling to algorithms \nand mechanism design, and including empirical studies.

Social choice theory provides insights into a variety of collective decision making settings, but nowadays some of its tenets are challenged by internet environments, which call for dynamic decision making under constantly changing preferences. In this paper we model the problem via Markov decision processes (MDP), where the states of the MDP coincide with preference profiles and a (deterministic, stationary) policy corresponds to a social choice function. We can therefore employ the axioms studied in the social choice literature as guidelines in the design of socially desirable policies. We present tractable algorithms that compute optimal policies under different prominent social choice constraints. Our machinery relies on techniques for exploiting symmetries and isomorphisms between MDPs.

By coordinating efforts from humans and machines, human computation systems can solve problems that machines cannot tackle alone. A general challenge is to design efficient human computation algorithms or workflows with which to coordinate the work of the crowd. We introduce a method for automated workflow synthesis aimed at ideally harnessing human efforts by learning about the crowd's performance on tasks and synthesizing an optimal workflow for solving a problem. We present experimental results for human sorting tasks, which demonstrate both the benefit of understanding and optimizing the structure of workflows based on observations. Results also demonstrate the benefits of using value of information to guide experiments for identifying efficient workflows with fewer experiments.

Agents are asked to rank two objects in a setting where effort is costly and agents differ in quality (which is the probability that they can identify the correct, ground truth, ranking). We study simple output-agreement mechanisms that pay an agent in the case she agrees with the report of another, and potentially penalizes for disagreement through a negative payment. Assuming access to a quality oracle, able to determine whether an agent's quality is above a given threshold, we design a payment scheme that aligns incentives so that agents whose quality is above this threshold participate and invest effort. Precluding negative payments leads the expected cost of this quality-oracle mechanism to increase by a factor of 2 to 5 relative to allowing both positive and negative payments. Dropping the assumption about access to a quality oracle, we further show that negative payments can be used to make agents with quality lower than the quality threshold choose to not to participate, while those above continue to participate and invest effort. Through the appropriate choice of payments, any design threshold can be achieved. This self-selection mechanism has the same expected cost as the cost-minimal quality-oracle mechanism, and thus when using the self-selection mechanism, perfect screening comes for free.

In this paper we propose a class of efficient Generalized Method-of-Moments(GMM) algorithms for computing parameters of the Plackett-Luce model, where the data consists of full rankings over alternatives. Our technique is based on breaking the full rankings into pairwise comparisons, and then computing parameters that satisfy a set of generalized moment conditions. We identify conditions for the output of GMM to be unique, and identify a general class of consistent and inconsistent breakings. We then show by theory and experiments that our algorithms run significantly faster than the classical Minorize-Maximization (MM) algorithm, while achieving competitive statistical efficiency.

We propose a model for demand estimation in multi-agent, differentiated product settings and present an estimation algorithm that uses reversible jump MCMC techniques to classify agents' types. Our model extends the popular setup in Berry, Levinsohn and Pakes (1995) to allow for the data-driven classification of agents' types using agent-level data. We focus on applications involving data on agents' ranking over alternatives, and present theoretical conditions that establish the identifiability of the model and uni-modality of the likelihood/posterior. Results on both real and simulated data provide support for the scalability of our approach.

In many natural settings, the analysis goal is not to characterize a single data set in isolation, but rather to understand the difference between one set of observations and another. For example, given a background corpus of news articles together with writings of a particular author, one may want a topic model that explains word patterns and themes specific to the author. Another example comes from genomics, in which biological signals may be collected from different regions of a genome, and one wants a model that captures the differential statistics observed in these regions. This paper formalizes this notion of contrastive learning for mixture models, and develops spectral algorithms for inferring mixture components specific to a foreground data set when contrasted with a background data set. The method builds on recent moment-based estimators and tensor decompositions for latent variable models, and has the intuitive feature of using background data statistics to appropriately modify moments estimated from foreground data. A key advantage of the method is that the background data need only be coarsely modeled, which is important when the background is too complex, noisy, or not of interest. The method is demonstrated on applications in contrastive topic modeling and genomic sequence analysis.

We develop an online mechanism for the allocation of an expiring resource to a dynamic agent population. Each agent has a non-increasing marginal valuation function for the resource, and an upper limit on the number of units that can be allocated in any period. We propose two versions on a truthful allocation mechanism. Each modifies the decisions of a greedy online assignment algorithm by sometimes cancelling an allocation of resources. One version makes this modification immediately upon an allocation decision while a second waits until the point at which an agent departs the market. Adopting a prior-free framework, we show that the second approach has better worst-case allocative efficiency and is more scalable. On the other hand, the first approach (with immediate cancellation) may be easier in practice because it does not need to reclaim units previously allocated. We consider an application to recharging plug-in hybrid electric vehicles (PHEVs). Using data from a real-world trial of PHEVs in the UK, we demonstrate higher system performance than a fixed price system, performance comparable with a standard, but non-truthful scheduling heuristic, and the ability to support 50% more vehicles at the same fuel cost than a simple randomized policy.

In mobile networks, authentication is a required primitive for most security protocols. Unfortunately, an adversary can monitor pseudonyms used for authentication to track the location of mobile nodes. A frequently proposed solution to protect location privacy suggests that mobile nodes collectively change their pseudonyms in regions called mix zones. This approach is costly. Self-interested mobile nodes might, thus, decide not to cooperate and jeopardize the achievable location privacy. In this paper, we analyze non-cooperative behavior of mobile nodes by using a game-theoretic model, where each player aims at maximizing its location privacy at a minimum cost. We obtain Nash equilibria in static n-player complete information games. As in practice mobile nodes do not know their opponents' payoffs, we then consider static incomplete information games. We establish that symmetric Bayesian-Nash equilibria exist with simple threshold strategies. By means of numerical results, we predict behavior of selfish mobile nodes. We then investigate dynamic games where players decide to change their pseudonym one after the other and show how this affects strategies at equilibrium. Finally, we design protocols-PseudoGame protocols-based on the results of our analysis and simulate their performance in vehicular network scenarios.

Schulze's rule and ranked pairs are two Condorcet methods that both satisfy many natural axiomatic properties. Schulze's rule is used in the elections of many organizations, including the Wikimedia Foundation, the Pirate Party of Sweden and Germany, the Debian project, and the Gento Project. Both rules are immune to control by cloning alternatives, but little is otherwise known about their strategic robustness, including resistance to manipulation by one or more voters, control by adding or deleting alternatives, adding or deleting votes, and bribery. Considering computational barriers, we show that these types of strategic behavior are NP-hard for ranked pairs (both constructive, in making an alternative a winner, and destructive, in precluding an alternative from being a winner). Schulze's rule, in comparison, remains vulnerable at least to constructive manipulation by a single voter and destructive manipulation by a coalition. As the first such polynomial-time rule known to resist all such manipulations, and considering also the broad axiomatic support, ranked pairs seems worthwhile to consider for practical applications.

Peer prediction mechanisms allow the truthful elicitation of private signals (e.g., experiences, or opinions) in regard to a true world state when this ground truth is unobservable. The original peer prediction method is incentive compatible for any number of agents n >= 2, but relies on a common prior, shared by all agents and the mechanism. The Bayesian Truth Serum (BTS) relaxes this assumption. While BTS still assumes that agents share a common prior, this prior need not be known to the mechanism. However, BTS is only incentive compatible for a large enough number of agents, and the particular number of agents required is uncertain because it depends on this private prior. In this paper, we present a robust BTS for the elicitation of binary information which is incentive compatible for every n >= 3, taking advantage of a particularity of the quadratic scoring rule. The robust BTS is the first peer prediction mechanism to provide strict incentive compatibility for every n >= 3 without relying on knowledge of the common prior. Moreover, and in contrast to the original BTS, our mechanism is numerically robust and ex post individually rational.

An important class of tasks that are underexplored in current human computation systems are complex tasks with global constraints. One example of such a task is itinerary planning, where solutions consist of a sequence of activities that meet requirements specified by the requester. In this paper, we focus on the crowdsourcing of such plans as a case study of constraint-based human computation tasks and introduce a collaborative planning system called Mobi that illustrates a novel crowdware paradigm. Mobi presents a single interface that enables crowd participants to view the current solution context and make appropriate contributions based on current needs. We conduct experiments that explain how Mobi enables a crowd to effectively and collaboratively resolve global constraints, and discuss how the design principles behind Mobi can more generally facilitate a crowd to tackle problems involving global constraints.

Random utility theory models an agents preferences on alternatives by drawing a real-valued score on each alternative (typically independently) from a parameterized distribution, and then ranking the alternatives according to scores. A special case that has received signicant attention is the Plackett-Luce model, for which fast inference methods for maximum likelihood estimators are available. This paper develops conditions on general random utility models that enable fast inference within a Bayesian framework through MC-EM, providing concave loglikelihood functions and bounded sets of global maxima solutions. Results on both real-world and simulated data provide support for the scalability of the approach and capability for model selection among general random utility models including Plackett-Luce.

In mechanism design it is typical to impose incentive compatibility and then derive an optimal mechanism subject to this constraint. By replacing the incentive compatibility requirement with the goal of minimizing expected ex post regret, we are able to adapt statistical machine learning techniques to the design of payment rules. This computational approach to mechanism design is applicable to domains with multi-dimensional types and situations where computational efficiency is a concern. Specifically, given an outcome rule and access to a type distribution, we train a support vector machine with a special discriminant function structure such that it implicitly establishes a payment rule with desirable incentive properties. We discuss applications to a multi-minded combinatorial auction with a greedy winner-determination algorithm and to an assignment problem with egalitarian outcome rule. Experimental results demonstrate both that the construction produces payment rules with low ex post regret, and that penalizing classification errors is effective in preventing failures of ex post individual rationality.

Faced with an intractable optimization problem, a common approach to computational mechanism design seeks a polynomial time approximation algorithm with an approximation guarantee. Rather than adopt this worst-case viewpoint, we introduce a new paradigm that seeks to obtain good performance on typical instances through a modification to the branch-and-bound search paradigm. Incentive compatibility in single-dimensional domains requires that an outcome improves monotonically for an agent as the agent's reported value increases. We obtain a monotone search algorithm by coupling an explicit sensitivity analysis on the decisions made during search with a correction to the outcome to ensure monotonicity. Extensive computational experiments on single-minded combinatorial auctions show better welfare performance than that available from existing approximation algorithms.

We study the problem of allocating multiple resources to agents with heterogeneous demands. Technological advances such as cloud computing and data centers provide a new impetus for investigating this problem under the assumption that agents demand the resources in fixed proportions, known in economics as Leontief preferences. In a recent paper, Ghodsi et al. [2011] introduced the dominant resource fairness (DRF) mechanism, which was shown to possess highly desirable theoretical properties under Leontief preferences. We extend their results in three directions. First, we show that DRF generalizes to more expressive settings, and leverage a new technical framework to formally extend its guarantees. Second, we study the relation between social welfare and properties such as truthfulness; DRF performs poorly in terms of social welfare, but we show that this is an unavoidable shortcoming that is shared by every mechanism that satisfies one of three basic properties. Third, and most importantly, we study a realistic setting that involves indivisibilities. We chart the boundaries of the possible in this setting, contributing a new relaxed notion of fairness and providing both possibility and impossibility results.

Despite the pervasiveness of markets in our lives, little is known about the role of user interfaces (UIs) in promoting good decisions in market domains. How does the way we display market information to end users, and the set of choices we offer, influence users' decisions? In this paper, we introduce a new research agenda on "market user interface design." Our goal is to find the optimal market UI, taking into account that users incur cognitive costs and are boundedly rational. Via lab experiments we systematically explore the market UI design space, and we study the automatic optimization of market UIs given a behavioral (quantal response) model of user behavior. Surprisingly, we find that the behaviorally-optimized UI performs worse than the standard UI, suggesting that the quantal response model did not predict user behavior well. Subsequently, we identify important behavioral factors that are missing from the user model, including loss aversion and position effects, which motivates follow-up studies. Furthermore, we find significant differences between individual users in terms of rationality. This suggests future research on personalized UI designs, with interfaces that are tailored towards each individual user's needs, capabilities, and preferences.

Reputation mechanisms at online opinion forums, such as Amazon Reviews, elicit ratings from users about their experience with different products. Crowdsourcing applications, such as image tagging on Amazon Mechanical Turk, elicit votes from users as to whether or not a job was duly completed. An important property in both settings is that the feedback received from users (agents) is truthful. The peer prediction method introduced by Miller et al. [2005] is a prominent theoretical mechanism for the truthful elicitation of reports. However, a significant obstacle to its application is that it critically depends on the assumption of a common prior amongst both the agents and the mechanism. In this paper, we develop a peer prediction mechanism for settings where the agents hold subjective and private beliefs about the state of the world and the likelihood of a positive signal given a particular state. Our shadow peer prediction mechanism exploits temporal structure in order to elicit two reports, a belief report and then a signal report, and it provides strict incentives for truthful reporting as long as the effect an agent's signal has on her posterior belief is bounded away from zero. Alternatively, this technical requirement on beliefs can be dispensed with by a modification in which the second report is a belief report rather than a signal report.

We consider the problem of fairly dividing a heterogeneous divisible good among agents with different preferences. Previous work has shown that envy-free allocations, i.e., where each agent prefers its own allocation to any other, may not be efficient, in the sense of maximizing the total value of the agents. Our goal is to pinpoint the most efficient allocations among all envy-free allocations. We provide tractable algorithms for doing so under different assumptions regarding the preferences of the agents.

We introduce a bidding language for expressing negative value externalities in position auctions for online advertising. The unit-bidder constraints (UBC) language allows a bidder to condition a bid on its allocated slot and on the slots allocated to other bidders. We introduce a natural extension of the Generalized Second Price (GSP) auction, the expressive GSP (eGSP) auction, that induces truthful revelation of constraints for a rich subclass of unit-bidder types, namely downward-monotonic UBC. We establish the existence of envy-free Nash equilibrium in eGSP under a further restriction to a subclass of exclusion constraints, for which the standard GSP has no pure strategy Nash equilibrium. The equilibrium results are obtained by reduction to equilibrium analysis for reserve price GSP (Even-Dar et al. 2008). In considering the winner determination problem, which is NP-hard, we bound the approximation ratio for social welfare in eGSP and provide parameterized complexity results.

The most prominent way to establish trust between buyers and sellers on online auction sites are reputation mechanisms. Two drawbacks of this approach are the reliance on the seller being long-lived and the susceptibility to whitewashing. In this paper, we introduce so-called escrow mechanisms that avoid these problems by installing a trusted intermediary which forwards the payment to the seller only if the buyer acknowledges that the good arrived in the promised condition. We address the incentive issues that arise and design an escrow mechanism that is incentive-compatible, efficient, interim individually rational and ex ante budget-balanced. In contrast to previous work on trust and reputation, our approach does not rely on knowing the sellers' cost functions or the distribution of buyer valuations.

A fundamental result in mechanism design theory, the so-called revelation principle, asserts that for many questions concerning the existence of mechanisms with a given outcome one can restrict attention to truthful direct-revelation mechanisms. In practice, however, many mechanisms use a restricted message space. This motivates the study of the tradeoffs involved in choosing simplified mechanisms, which can sometimes bring benefits in precluding bad or promoting good equilibria, and other times impose costs on welfare and revenue. We study the simplicity-expressiveness tradeoff in two representative settings, sponsored search auctions and combinatorial auctions, each being a canonical example for complete information and incomplete information analysis, respectively. We observe that the amount of information available to the agents plays an important role for the tradeoff between simplicity and expressiveness.

In kidney exchanges, hospitals share patient lists and receive transplantations. A kidney-paired donation (KPD) mechanism needs to promote full sharing of information about donor-patient pairs, and identify a Pareto efficient outcome that also satisfies participation constraints of hospitals. We introduce a random graph model of the KPD exchange and then fully characterize the structure of the efficient outcome and the expected number of transplantations that can be performed. Random graph theory allows early experimental results to be explained analytically, and enables the study of participation incentives in a methodological way. We derive a square-root law between the welfare gains from sharing patient-donor pairs in a central pool and the individual sizes of hospitals, illustrating the urgent need for the nationwide expansion of such programs. Finally, we establish through theoretical and computational analysis that enforcing simple individual rationality constraints on the outcome can mitigate the negative impact of strategic behavior by hospitals.

Cake cutting is a common metaphor for the division of a heterogeneous divisible good. There are numerous papers that study the problem of fairly dividing a cake; a small number of them also take into account self-interested agents and consequent strategic issues, but these papers focus on fairness and consider a strikingly weak notion of truthfulness. In this paper we investigate the problem of cutting a cake in a way that is truthful and fair, where for the first time our notion of dominant strategy truthfulness is the ubiquitous one in social choice and computer science. We design both deterministic and randomized cake cutting algorithms that are truthful and fair under different assumptions with respect to the valuation functions of the agents.

The next decade will see an abundance of new intelligent systems, many of which will be market-based. Soon, users will interact with many new markets, perhaps without even knowing it: when driving their car, when listening to a song, when backing up their files, or when surfing the web. We argue that these new systems can only be successful if a new approach is chosen towards designing them. In this paper we introduce the general problem of "Hidden Market Design." The design of a "weakly hidden" market involves reducing some of the market complexities and providing a user interface (UI) that makes the interaction seamless for the user. A "strongly hidden market" is one where some semantic aspect of a market is hidden altogether (e.g., budgets, prices, combinatorial constraints). We show that the intersection of UI design and market design is of particular importance for this research agenda. To illustrate hidden market design, we give a series of potential applications. We hope that the problem of hidden market design will inspire other researchers and lead to new research in this direction, paving the way for more successful market-based systems in the future.

In distributed work systems, individual users perform work for other users. A significant challenge in these systems is to provide proper incentives for users to contribute as much work as they consume, even when monitoring is not possible. We formalize the problem of designing "incentive-compatible accounting mechanisms" that measure the net contributions of users, despite relying on voluntary reports. We introduce the Drop-Edge Mechanism that removes any incentive for a user to manipulate via misreports about work contributed or consumed. We prove that Drop-Edge provides a good approximation to a user's net contribution, and is accurate in the limit as the number of users grows. We demonstrate very good welfare properties in simulation compared to an existing, manipulable mechanism. In closing, we show the power of sybil attacks in accounting mechanisms and discuss our ongoing work, including a real-world implementation and evaluation of the Drop-Edge Mechanism in a BitTorrent client.

The use of simple auction mechanisms like the GSP in online advertising can lead to significant loss of efficiency and revenue when advertisers have rich preferences — even simple forms of expressiveness like budget constraints can lead to suboptimal outcomes. While the optimal allocation of inventory can provide greater efficiency and revenue, natural formulations of the underlying optimization problems grow exponentially in the number of features of interest, presenting a key practical challenge. To address this problem, we propose a means for automatically partitioning inventory into abstract channels so that the least relevant features are ignored. Our approach, based on LP/MIP column and constraint generation, dramatically reduces the size of the problem, thus rendering optimization computationally feasible at practical scales. Our algorithms allow for principled tradeoffs between tractability and solution quality. Numerical experiments demonstrate the computational practicality of our approach as well as the quality of the resulting abstractions.

We study a problem of dynamic allocation without money. Agents have arrivals and departures and strict preferences over items. Strategyproofness requires the use of an arrival-priority serial-dictatorship (APSD) mechanism, which is ex post Pareto efficient but has poor ex ante efficiency as measured through average rank efficiency. We introduce the scoring-rule (SR) mechanism, which biases in favor of allocating items that an agent values above the population consensus. The SR mechanism is not strategyproof but has tolerable manipulability in the sense that: (i) if every agent optimally manipulates, it reduces to APSD, and (ii) it significantly outperforms APSD for rank efficiency when only a fraction of agents are strategic. The performance of SR is also robust to mistakes by agents that manipulate on the basis of inaccurate information about the popularity of items.

In mobile networks, authentication is a required primitive for the majority of security protocols. However, an adversary can track the location of mobile nodes by monitoring pseudonyms used for authentication. A frequently proposed solution to protect location privacy suggests that mobile nodes collectively change their pseudonyms in regions called mix zones. Because this approach is costly, self-interested mobile nodes might decide not to cooperate and could thus jeopardize the achievable location privacy. In this paper, we analyze the non-cooperative behavior of mobile nodes by using a game-theoretic model, where each player aims at maximizing its location privacy at a minimum cost. We first analyze the Nash equilibria in n-player complete information games. Because mobile nodes in a privacy-sensitive system do not know their opponents' payoffs, we then consider incomplete information games. We establish that symmetric Bayesian-Nash equilibria exist with simple threshold strategies in n-player games and derive the equilibrium strategies. By means of numerical results, we show that mobile nodes become selfish when the cost of changing pseudonyms is small, whereas they cooperate more when the cost of changing pseudonyms increases. Finally, we design a protocol - the PseudoGame protocol - based on the results of our analysis.

End-to-end packet delivery in the Internet is achieved through a system of interconnections between the network domains of independent entities called autonomous systems (ASes). Inter-domain connections are the result of a complex, dynamic process of negotiated business relationships between pairs of ASes. We present an economically-principled generative model for autonomous system graph connectivity. While there is already a large literature devoted to understanding Internet connectivity at the AS level, many of these models are either static or based on generalized stochastics.

We exploit methods of sample-based stochastic optimization for the purpose of strategyproof dynamic, multi-unit auctions. There are no analytic characterizations of optimal policies for this domain and thus a heuristic approach, such as that proposed here, seems necessary in practice. Following the suggestion of Parkes and Duong [17], we perform sensitivity analysis on the allocation decisions of an online algorithm for stochastic optimization, and correct the decisions to enable a strategyproof auction. In applying this approach to the allocation of non-expiring goods, the technical problem that we must address is related to achieving strategyproofness for reports of departure. This cannot be achieved through self-correction without canceling many allocation decisions, and must instead be achieved by first modifying the underlying algorithm. We introduce the NowWait method for this purpose, prove its successful interfacing with sensitivity analysis and demonstrate good empirical performance. Our method is quite general, requiring a technical property of uncertainty independence, and that values are not too positively correlated with agent patience. We also show how to incorporate "virtual valuations" in order to increase the seller's revenue.

In this paper, we provide a simple game-theoretic model of an online question and answer forum. We focus on factual questions in which user responses aggregate while a question remains open. Each user has a unique piece of information and can decide when to report this information. The asker prefers to receive information sooner rather than later, and will stop the process when satisfied with the cumulative value of the posted information. We consider two distinct cases: a complements case, in which each successive piece of information is worth more to the asker than the previous one; and a substitutes case, in which each successive piece of information is worth less than the previous one. A best-answer scoring rule is adopted to model Yahoo! Answers, and is effective for substitutes information, where it isolates an equilibrium in which all users respond in the first round. But we find that this rule is ineffective for complements information, isolating instead an equilibrium in which all users respond in the final round. In addressing this, we demonstrate that an approval-voting scoring rule and a proportional-share scoring rule can enable the most efficient equilibrium with complements information, under certain conditions, by providing incentives for early responders as well as the user who submits the final answer.

Policy teaching considers a Markov Decision Process setting in which an interested party aims to influence an agent's decisions by providing limited incentives. In this paper, we consider the specific objective of inducing a pre-specified desired policy. We examine both the case in which the agent's reward function is known and unknown to the interested party, presenting a linear program for the former case and formulating an active, indirect elicitation method for the latter. We provide conditions for logarithmic convergence, and present a polynomial time algorithm that ensures logarithmic convergence with arbitrarily high probability. We also offer practical elicitation heuristics that can be formulated as linear programs, and demonstrate their effectiveness on a policy teaching problem in a simulated ad-network setting. We extend our methods to handle partial observations and partial target policies, and provide a game-theoretic interpretation of our methods for handling strategic agents.

We consider the amount of communication required to verify the outcome of the Vickrey-Clarke-Groves (VCG) mechanism: an efficient allocation together with incentivizing VCG payments. We compare this to the communication required to verify the efficient decision rule alone, to assess the overhead imposed by VCG payments. Our characterizations are obtained by leveraging a connection between the VCG outcome and a price equilibrium concept known as universal competitive equilibrium. We consider four related environments within a common framework: the classic single-item setting, the multi-unit setting with decreasing marginal values, the classic assignment problem with unit-demand valuations, and the multi-unit assignment problem with substitutes valuations. We find that the single-unit settings have zero overhead, whereas the multi-unit settings can have significant positive overhead. With multiple units, the naïve VCG protocol that runs several efficient protocols in sequence (one with all agents, and ones with an agent removed, for each agent) is asymptotically optimal for several parameter settings of the number of agents, commodities, and units.

We present the design and analysis of the first fully expressive, iterative combinatorial exchange (ICE). The exchange incorporates a tree-based bidding language (TBBL) that is concise and expressive for CEs. Bidders specify lower and upper bounds in TBBL on their value for different trades and refine these bounds across rounds. These bounds allow price discovery and useful preference elicitation in early rounds, and allow termination with an efficient trade despite partial information on bidder valuations. All computation in the exchange is carefully optimized to exploit the structure of the bid-trees and to avoid enumerating trades. A proxied interpretation of a revealed-preference activity rule, coupled with simple linear prices, ensures progress across rounds. The exchange is fully implemented, and we give results demonstrating several aspects of its scalability and economic properties with simulated bidding strategies.

In the efficient social choice problem, the goal is to assign values, subject to side constraints, to a set of variables to maximize the total utility across a population of agents, where each agent has private information about its utility function. In this paper we model the social choice problem as a distributed constraint optimization problem (DCOP), in which each agent can communicate with other agents that share an interest in one or more variables. Whereas existing DCOP algorithms can be easily manipulated by an agent, either by misreporting private information or deviating from the algorithm, we introduce M-DPOP, the first DCOP algorithm that provides a faithful distributed implementation for efficient social choice. This provides a concrete example of how the methods of mechanism design can be unified with those of distributed optimization. Faithfulness ensures that no agent can benefit by unilaterally deviating from any aspect of the protocol, neither information-revelation, computation, nor communication, and whatever the private information of other agents. We allow for payments by agents to a central bank, which is the only central authoritythat we require. To achieve faithfulness, we carefully integrate the Vickrey-Clarke-Groves (VCG) mechanism with the DPOP algorithm, such that each agent is only asked to perform computation, report information, and send messages that is in its own best interest. Determining agent i's payment requires solving the social choice problem without agent i. Here, we present a method to reuse computation performed in solving the main problem in a way that is robust against manipulation by the excluded agent. Experimental results on structured problems show that as much as 87% of the computation required for solving the marginal problems can be avoided by re-use, providing very good scalability in the number of agents. On unstructured problems, we observe a sensitivity of M-DPOP to the density of the problem, and we show that reusability decreases from almost 100% for very sparse problems to around 20% for highly connected problems. We close with a discussion of the features of DCOP that enable faithful implementations in this problem, the challenge of reusing computation from the main problem to marginal problems in other algorithms such as ADOPT and OptAPO, and the prospect of methods to avoid the welfare loss that can occur because of the transfer of payments to the bank.

In this paper we present and evaluate a general framework for the design of truthful auctions for matching agents in a dynamic, two-sided market. A single commodity, such as a resource or a task, is bought and sold by multiple buyers and sellers that arrive and depart over time. Our algorithm, Chain, provides the first framework that allows a truthful dynamic double auction (DA) to be constructed from a truthful, single-period (i.e. static) double-auction rule. The pricing and matching method of the Chain construction is unique amongst dynamic-auction rules that adopt the same building block. We examine experimentally the allocative efficiency of Chain when instantiated on various single-period rules, including the canonical McAfee double-auction rule. For a baseline we also consider non-truthful double auctions populated with ``zero-intelligence plus"-style learning agents. Chain-based auctions perform well in comparison with other schemes, especially as arrival intensity falls and agent valuations become more volatile.

Consider an open infrastructure in which anyone can deploy mechanisms to support automated decision making and coordination amongst self-interested computational agents. Strategyproofness is a central property in the design of such mechanisms, allowing participants to maximize their individual benefit by reporting truthful private information about preferences and capabilities and without modeling or reasoning about the behavior of other agents. But, why should participants trust that a mechanism is strategyproof? We address this problem, proposing and describing a passive verifier, able to monitor the inputs and outputs of mechanisms and verify the strategyproofness, or not, of a mechanism. Useful guarantees are available to participants before the behavior of the mechanism is completely known, and metrics are introduced to provide a measure of partial verification. Experimental results demonstrate the effectiveness of our method.

We present a practical system for conducting sealed-bid auctions that preserves the secrecy of the bids while providing for verifiable correctness and trustworthiness of the auction. The auctioneer must accept all bids submitted and follow the published rules of the auction. No party receives any useful information about bids before the auction closes and no bidder is able to change or repudiate her bid. Our solution uses Paillier's homomorphic encryption scheme [25] for zero knowledge proofs of correctness. Only minimal cryptographic technology is required of bidders; instead of employing complex interactive protocols or multi-party computation, the single auctioneer computes optimal auction results and publishes proofs of the results' correctness. Any party can check these proofs of correctness via publicly verifiable computations on encrypted bids. The system is illustrated through application to first-price, uniform-price and second-price auctions, including multi-item auctions. Our empirical results demonstrate the practicality of our method: auctions with hundreds of bidders are within reach of a single PC, while a modest distributed computing network can accommodate auctions with thousands of bids.

Bidders on eBay have no dominant bidding strategy when faced with multiple auctions each offering an item of interest. As seen through an analysis of 1,956 auctions on eBay for a Dell E193FP LCD monitor, some bidders win auctions at prices higher than those of other available auctions, while others never win an auction despite placing bids in losing efforts that are greater than the closing prices of other available auctions. These misqueues in strategic behavior hamper the efficiency of the system, and in so doing limit the revenue potential for sellers. This paper proposes a novel options-based extension to eBay's proxy-bidding system that resolves this strategic issue for buyers in commoditized markets. An empirical analysis of eBay provides a basis for computer simulations that investigate the market effects of the options-based scheme, and demonstrates that the options-based scheme provides greater efficiency than eBay, while also increasing seller revenue.

Given a collection of selfish agents who wish to establish links to route traffic among themselves, the set of equilibrium network topologies may appear quite different from the centrally enforced optimum. We study the quality (price of anarchy) of equilibrium networks in a game where links require the consent of both participants and are negotiated bilaterally and compare these networks to those generated by an earlier model due to Fabrikant et al. [6] in which links are formed unilaterally. We provide a characterization of stable and efficient networks in the bilateral network formation game, show that the set of stable networks is richer than those in the unilateral game, and that all stable networks of the unilateral game are also stable in the bilateral game. We also provide an upper and lower bound on the price of anarchy (tight in the size of the network n but not the link cost α) of the bilateral game and show that the worst-case price of anarchy of the bilateral model is worse than for the unilateral model. A careful empirical analysis demonstrates that the average price of anarchy is better in the bilateral connection game than in the unilateral game for small link costs but worse as links become more expensive. In the process, a powerful equivalence between link-based graph stability and two game-theoretic equilibrium notions is also discussed. The equivalence establishes necessary and sufficient conditions for an equilibrium in the bilateral game that helps provide a partial geometric characterization of equilibrium graphs.

This paper concerns the design of mechanisms for online scheduling in which agents bid for access to a re-usable resource such as processor time or wireless network access. Each agent is assumed to arrive and depart dynamically, and in the basic model require the resource for one unit of time. We seek mechanisms that are truthful in the sense that truthful revelation of arrival, departure and value information is a dominant strategy, and that are online in the sense that they make allocation decisions without knowledge of the future. First, we provide two characterizations for the class of truthful online allocation rules. The characterizations extend beyond the typical single-parameter settings, and formalize the role of restricted misreporting in reversing existing price-based characterizations. Second, we present an online auction for unit-length jobs that achieves total value that is 2-competitive with the maximum offline value. We prove that no truthful deterministic online mechanism can achieve a better competitive ratio. Third, we consider revenue competitiveness and prove that no deterministic truthful online auction has revenue that is constant-competitive with that of the offline Vickrey-Clarke-Groves (VCG) mechanism We provide a randomized online auction that achieves a competitive ratio of O(log h), where h is the ratio of maximum value to minimum value among the agents; this mechanism does not require prior knowledge of h. Finally, we generalize our model to settings with multiple re-usable goods and to agents with different job lengths.

We present the first design for a fully expressive iterative combinatorial exchange (ICE). The exchange incorporates a tree-based bidding language that is concise and expressive for CEs. Bidders specify lower and upper bounds on their value for different trades. These bounds allow price discovery and useful preference elicitation in early rounds, and allow termination with an efficient trade despite partial information on bidder valuations. All computation in the exchange is carefully optimized to exploit the structure of the bid-trees and to avoid enumerating trades. A proxied interpretation of a revealed-preference activity rule ensures progress across rounds. A VCG-based payment scheme that has been shown to mitigate opportunities for bargaining and strategic behavior is used to determine final payments. The exchange is fully implemented and in a validation phase.

Online mechanism design (OMD) addresses the problem of sequential decision making in a stochastic environment with multiple self-interested agents. The goal in OMD is to make value-maximizing decisions despite this self-interest. In previous work we presented a Markov decision pro- cess (MDP)-based approach to OMD in large-scale problem domains. In practice the underlying MDP needed to solve OMD is too large and hence the mechanism must consider approximations. This raises the pos- sibility that agents may be able to exploit the approximation for selfish gain. We adopt sparse-sampling-based MDP algorithms to implement - efficient policies, and retain truth-revelation as an approximate Bayesian- Nash equilibrium. Our approach is empirically illustrated in the context of the dynamic allocation of WiFi connectivity to users in a coffeehouse. 1 Introduction Mechanism design (MD) is concerned with the problem of providing incentives to im- plement desired system-wide outcomes in systems with multiple self-interested agents. Agents are assumed to have private information, for example about their utility for differ- ent outcomes and about their ability to implement different outcomes, and act to maximize their own utility. The MD approach to achieving multiagent coordination supposes the ex- istence of a center that can receive messages from agents and implement an outcome and collect payments from agents. The goal of MD is to implement an outcome with desired system-wide properties in a game-theoretic equilibrium. Classic mechanism design considers static systems in which all agents are present and a one-time decision is made about an outcome. Auctions, used in the context of resource- allocation problems, are a standard example. Online mechanism design [1] departs from this and allows agents to arrive and depart dynamically requiring decisions to be made with uncertainty about the future. Thus, an online mechanism makes a sequence of decisions without the benefit of hindsight about the valuations of the agents yet to arrive. Without the issue of incentives, the online MD problem is a classic sequential decision problem. In prior work [6], we showed that Markov decision processes (MDPs) can be used to define an online Vickrey-Clarke-Groves (VCG) mechanism [2] that makes truth-revelation by the agents (called incentive-compatibility) a Bayesian-Nash equilibrium [5] and implements a policy that maximizes the expected summed value of all agents. This online VCG model differs from the line of work in online auctions, introduced by Lavi and Nisan [4] in that it assumes that the center has a model and it handles a general decision space and any decision horizon. Computing the payments and allocations in the online VCG mechanism involves solving the MDP that defines the underlying centralized (ignoring self-interest) decision making problem. For large systems, the MDPs that need to be solved exactly become large and thus computationally infeasible. In this paper we consider the case where the underlying centralized MDPs are indeed too large and thus must be solved approximately, as will be the case in most real applications. Of course, there are several choices of methods for solving MDPs approximately. We show that the sparse-sampling algorithm due to Kearns et al. [3] is particularly well suited to online MD because it produces the needed local approximations to the optimal value and action efficiently. More challengingly, regardless of our choice the agents in the system can exploit their knowledge of the mechanism's approximation algorithm to try and "cheat" the mechanism to further their own selfish interests. Our main contribution is to demonstrate that our new approximate online VCG mechanism has truth-revelation by the agents as an -Bayesian-Nash equilibrium (BNE). This approximate equilibrium supposes that each agent is indifferent to within an expected utility of , and will play a truthful strategy in best- response to truthful strategies of other agents if no other strategy can improve its utility by more than . For any , our online mechanism has a run-time that is independent of the number of states in the underlying MDP, provides an -BNE, and implements a policy with expected value within of the optimal policy's value. Our approach is empirically illustrated in the context of the dynamic allocation of WiFi con- nectivity to users in a coffeehouse. We demonstrate the speed-up introduced with sparse- sampling (compared with policy calculation via value-iteration), as well as the economic value of adopting an MDP-based approach over a simple fixed-price approach. 2 Preliminaries Here we formalize the multiagent sequential decision problem that defines the online mech- anism design (OMD) problem. The approach is centralized. Each agent is asked to report its private information (for instance about its value and its capabilities) to a central planner or mechanism upon arrival. The mechanism implements a policy based on its view of the state of the world (as reported by agents). The policy defines actions in each state, and the assumption is that all agents acquiesce to the decisions of the planner. The mechanism also collects payments from agents, which can themselves depend on the reports of agents. Online Mechanism Design We consider a finite-horizon problem with a set T of time points and a sequence of decisions k = {k1, . . . , kT }, where kt Kt and Kt is the set of feasible decisions in period t. Agent i I arrives at time ai T , departs at time li T , and has value vi(k) 0 for a sequence of decisions k. By assumption, an agent has no value for decisions outside of interval [ai, li]. Agents also face payments, which can be col- lected after an agent's departure. Collectively, information i = (ai, li, vi) defines the type of agent i with i . Agent types are sampled i.i.d. from a probability distribution f (), assumed known to the agents and to the central mechanism. Multiple agents can arrive and depart at the same time. Agent i, with type i, receives utility ui(k, p; i) = vi(k; i) - p, for decisions k and payment p. Agents are modeled as expected-utility maximizers. Definition 1 (Online Mechanism Design) The OMD problem is to implement the sequence of decisions that maximizes the expected summed value across all agents in equilibrium, given self-interested agents with private information about valuations. In economic terms, an optimal (value-maximizing) policy is the allocatively-efficient, or simply the efficient policy. Note that nothing about the OMD models requires centralized execution of the joint plan. Rather, the agents themselves can have capabilities to perform actions and be asked to perform particular actions by the mechanism. The agents can also have private information about the actions that they are able to perform. Using MDPs to Solve Online Mechanism Design. In the MDP-based approach to solv- ing the OMD problem the sequential decision problem is formalized as an MDP with the state at any time encapsulating both the current agent population and constraints on current decisions as reflected by decisions made previously. The reward function in the MDP is simply defined to correspond with the total reported value of all agents for all sequences of decisions. Given types i f () we define an MDP, Mf , as follows. Define the state of the MDP at time t as the history-vector ht = (1, . . . , t; k1, . . . , kt-1), to include the reported types up to and including period t and the decisions made up to and including period t - 1.1 The set of all possible states at time t is denoted Ht. The set of all possible states across all time is H = T +1 H t=1 t. The set of decisions available in state ht is Kt(ht). Given a decision kt Kt(ht) in state ht, there is some probability distribution Prob(ht+1|ht, kt) over possible next states ht+1. In the setting of OMD, this probability distribution is determined by the uncertainty on new agent arrivals (as represented within f ()), together with departures and the impact of decision kt on state. The payoff function for the induced MDP is defined to reflect the goal of maximizing the total expected reward across all agents. In particular, payoff Ri(ht, kt) = vi(kt; i) - vi(kt-1; i) becomes available from agent i upon taking action kt in state ht. With this, we have Ri(h t=1 t, kt) = vi(k ; i), for all periods to provide the required cor- respondence with agent valuations. Let R(ht, kt) = Ri(h i t, kt), denote the payoff obtained from all agents at time t. Given a (nonstationary) policy = {1, 2, . . . , T } where t : Ht Kt, an MDP defines an MDP-value function V as follows: V (ht) is the expected value of the summed payoff obtained from state ht onwards under policy , i.e., V (ht) = E{R(ht, (ht)) + R(ht+1, (ht+1)) + + R(hT , (hT ))}. An optimal policy is one that maximizes the MDP-value of every state in H. The optimal MDP-value function V can be computed by value-iteration, and is defined so that V (h) = maxkK P rob(h |h, k)V (h )] for t = T - t (h) [R(h, k) + h Ht+1 1, T - 2, . . . , 1 and all h Ht, with V (h HT ) = maxkKT (h) R(h, k). Given the optimal MDP-value function, the optimal policy is derived as follows: for t < T , policy (h Ht) chooses action arg maxkK P rob(h |h, k)V (h )] t (h) [R(h, k) + h Ht+1 and (h HT ) = arg maxkKT (h) R(h, k). Let ^ t denote reported types up to and including period t . Let Ri (^ t t ; ) denote the total reported reward to agent i up to and including period t . The commitment period for agent i is defined as the first period, mi, for which t mi, Ri (^ ; ) = Ri (^ ; ) , for any types still to m m m i i t i >mi >mi arrive. This is the earliest period in which agent i's total value is known with certainty. Let ht (^ t ; ) denote the state in period t given reports ^ t . Let ^ t \i = ^ t \ ^ i. Definition 2 (Online VCG mechanism) Given history h H, mechanism Mvcg = (; , pvcg) implements policy and collects payment, pvcg(^ ; ) = Ri (^ ; ) - V (h (^ ; )) - V (h (^ i mi m m ^ a ^ a ^ a ^ a i i i i i i \i ; )) (1) from agent i in some period t mi. 1Using histories as state will make the state space very large. Often, there will be some function g for which g(h) is a sufficient statistic for all possible states h. We ignore this possibility here. Agent i's payment is equal to its reported value discounted by the expected marginal value that it will contribute to the system as determined by the MDP-value function for the policy in its arrival period. The incentive-compatibility of the Online VCG mechanism requires that the MDP satisfies stalling which requires that the expected value from the optimal policy in every state in which an agent arrives is at least the expected value from following the optimal action in that state as though the agent had never arrived and then returning to the optimal policy. Clearly, property Kt(ht) Kt(ht \ i) in any period t in which i has just arrived is sufficient for stalling. Stalling is satisfied whenever an agent's arrival does not force a change in action on a policy. Theorem 1 (Parkes & Singh [6]) An online VCG mechanism, Mvcg = (; , pvcg), based on an optimal policy for a correct MDP model that satisfies stalling is Bayesian- Nash incentive compatible and implements the optimal MDP policy. 3 Solving Very Large MDPs Approximately From Equation 1, it can be seen that making outcome and payment decisions at any point in time in an online VCG mechanism does not require a global value function or a global policy. Unlike most methods for approximately solving MDPs that compute global approx- imations, the sparse-sampling methods of Kearns et al. [3] compute approximate values and actions for a single state at a time. Furthermore, sparse-sampling methods provide approx- imation guarantees that will be important to establish equilibrium properties -- they can compute an -approximation to the optimal value and action in a given state in time inde- pendent of the size of the state space (though polynomial in 1 and exponential in the time horizon). Thus, sparse-sampling methods are particularly suited to approximating online VCG and we adopt them here. The sparse-sampling algorithm uses the MDP model Mf as a generative model, i.e., as a black box from which a sample of the next-state and reward distributions for any given state-action pair can be obtained. Given a state s and an approximation parameter , it computes an -accurate estimate of the optimal value for s as follows. We make the param- eterization on explicit by writing sparse-sampling( ). The algorithm builds out a depth-T sampled tree in which each node is a state and each node's children are obtained by sam- pling each action in that state m times (where m is chosen to guarantee an approximation to the optimal value of s), and each edge is labeled with the sample reward for that transi- tion. The algorithm computes estimates of the optimal value for nodes in the tree working backwards from the leaves as follows. The leaf-nodes have zero value. The value of a node is the maximum over the values for all actions in that node. The value of an action in a node is the summed value of the m rewards on the m outgoing edges for that action plus the summed value of the m children of that node. The estimated optimal value of state s is the value of the root node of the tree. The estimated optimal action in state s is the action that leads to the largest value for the root node in the tree. Lemma 1 (Adapted from Kearns, Mansour & Ng [3]) The sparse-sampling( ) algorithm, given access to a generative model for any n-action MDP M , takes as input any state s S and any > 0, outputs an action, and satisfies the following two conditions: (Running Time) The running time of the algorithm is O((nC)T ), where C = f (n, 1 , Rmax, T ) and f is a polynomial function of the approximation parameter 1 , the number of actions n, the largest expected reward in a state Rmax and the horizon T . In particular, the running time has no dependence on the number of states. (Near-Optimality) The value function of the stochastic policy implemented by the sparse-sampling( ) algorithm, denoted V ss, satisfies |V (s) - V ss(s)| si- multaneously for all states s S. It is straightforward to derive the following corollary from the proof of Lemma 1 in [3]. Corollary 1 The value function computed by the sparse-sampling( ) algorithm, denoted ^ V ss, is near-optimal in expectation, i.e., |V (s) - E{ ^ V ss(s)}| simultaneously for all states s S and where the expectation is over the randomness introduced by the sparse- sampling( ) algorithm. 4 Approximately Efficient Online Mechanism Design In this section, we define an approximate online VCG mechanism and consider the effect on incentives of substituting the sparse-sampling( ) algorithm into the online VCG mech- anism. We model agents as indifferent between decisions that differ by at most a utility of > 0, and consider an approximate Bayesian-Nash equilibrium. Let vi(; ) denote the final value to agent i after reports given policy . Definition 3 (approximate BNE) Mechanism Mvcg = (, , pvcg) is -Bayesian-Nash in- centive compatible if E| {vi(; ) - pvcg(; )} + E {vi(-i, ^ i; ) - pvcg(-i, ^ i; )}(2) | t i t i where agent i with type i arrives in period t , and with the expectation taken over future types given current reports t . In particular, when truth-telling is an -BNE we say that the mechanism is -BNE incentive compatible and no agent can improve its expected utility by more than > 0, for any type, as long as other agents are bidding truthfully. Equivalently, one can interpret an -BNE as an exact equilibrium for agents that face a computational cost of at least to compute the exact BNE. Definition 4 (approximate mechanism) A sparse-sampling( ) based approximate online VCG mechanism, Mvcg( ) = (; ~ , ~ pvcg), uses the sparse-sampling( ) algorithm to imple- ment stochastic policy ~ and collects payment ~ pvcg(^ ; ~ ) = Ri (^ ; ~ ) - ^ V ss(h (^ ; ~ )) - ^ V ss(h (^ i mi m m ^ a ^ a ^ a ^ a i i i i i i \i ; ~ )) from agent i in some period t mi, for commitment period mi. Our proof of incentive-compatibility first demonstrates that an approximate delayed VCG mechanism [1, 6] is -BNE. With this, we demonstrate that the expected value of the pay- ments in the approximate online VCG mechanism is within 3 of the payments in the approximate delayed VCG mechanism. The delayed VCG mechanism makes the same decisions as the online VCG mechanism, except that payments are delayed until the final period and computed as: pDvcg(^ ; ) = Ri (^ ; ) - R i T T ( ^ ; ) - RT (^ -i; ) (3) where the discount is computed ex post, once the effect of an agent on the system value is known. In an approximate delayed-VCG mechanism, the role of the sparse-sampling algorithm is to implement an approximate policy, as well as counterfactual policies for the worlds -i without each agent i in turn. The total reported reward to agents = i over this counterfactual series of states is used to define the payment to agent i. Lemma 2 Truthful bidding is an -Bayesian-Nash equilibrium in the sparse-sampling( ) based approximate delayed-VCG mechanism. Proof: Let ~ denote the approximate policy computed by the sparse-sampling algorithm. Assume agents = i are truthful. Now, if agent i bids truthfully its expected utility is E| {v Rj (; ~ ) - Rj ( a i(; ~ ) + T T -i; ~ )} (4) i j=i j=i where the expectation is over both the types yet to be reported and the random- ness introduced by the sparse-sampling( ) algorithm. Substituting R V (ha ( ; ~ )) - V ss(h ( i ai ai ai\i; ~ )) - (5) because V ss(ha ( ; ~ )) V (h ( ; ~ )) - by Lemma 1. Now, ignore term i ai ai ai RT (-i; ~ ) in Equation (4), which is independent of agent i's bid ^ i, and consider the maximal expected utility to agent i from some non-truthful bid. The effect of ^ i on the first two terms is indirect, through a change in the policy for periods ai. An agent can change the policy only indirectly, by changing the center's view of the state by misreporting its type. By definition, the agent can do no better than selecting optimal policy , which is defined to maximize the expected value of the first two terms. Putting this together, the expected utility from ^ i is at most V (ha ( ; ~ )) - V ss(h ( i ai ai ai\i; ~ )) and at most better than that from bidding truthfully. Theorem 2 Truthful bidding is an 4 -Bayesian-Nash equilibrium in the sparse- sampling( ) based approximate online VCG mechanism. Proof: Assume agents = i bid truthfully, and consider report ^ i. Clearly, the policy implemented in the approximate online-VCG mechanism is the same as in the delayed- VCG mechanism for all ^ i. Left to show is that the expected value of the payments are within 3 for all ^ i. From this we conclude that the expected utility to agent i in the approximate-VCG mechanism is always within 3 of that in the approximate delayed-VCG mechanism, and therefore 4 -BNE by Lemma 2. The expected payment in the approximate online VCG mechanism is E| {Ri (^ ; ~ )} - E{ ^ V ss(h (^ ; ~ )} - E{ ^ V ss(h (^ a T ^ ai ^ ai ^ ai ^ ai\i; ~ )} i The value function computed by the sparse-sampling( ) algorithm is a random variable to agent i at the time of bidding, and the second and third expectations are over the random- ness introduced by the sparse-sampling( ) algorithm. The first term is the same as in the payment in the approximate delayed-VCG mechanism. By Corollary 1, the value function estimated in the sparse-sampling( ) is near-optimal in expectation and the total of the sec- ond two terms is at least V (h^a (^ (^ ; )) - 2 . Ignoring the first i ^ ai\i; )) - V (h^ ai ^ ai term in pDvcg, the expected payment in the approximate delayed-VCG mechanism is no i more than V (h^a (^ (^ ; )) - ) because of the near-optimality i ^ ai\i; )) - (V (h^ ai ^ ai of the value function of the stochastic policy (Lemma 1). Putting this together, we have a maximum difference in expected payments of 3 . Similar analysis yields a maximum dif- ference of 3 when an upper-bound is taken on the payment in the online VCG mechanism and compared with a lower-bound on the payment in the delayed mechanism. Theorem 3 For any parameter > 0, the sparse-sampling( ) based approximate online VCG mechanism has -efficiency in an 4 -BNE. 5 Empirical Evaluation of Approximate Online VCG The WiFi Problem. The WiFi problem considers a fixed number of channels C with a random number of agents (max A) that can arrive per period. The time horizon T = 50. Agents demand a single channel and arrive with per-unit value, distributed i.i.d. V = {v1, . . . , vk} and duration in the system, distributed i.i.d. D = {d1, . . . , dl}. The value model requires that any allocation to agent i must be for contiguous periods, and be made while the agent is present (i.e., during periods [t, ai + di], for arrival ai and duration di). An agent's value for an allocation of duration x is vix where vi is its per-unit value. Let dmax denote the maximal possible allocated duration. We define the following MDP components: State space: We use the following compact, sufficient, statistic of history: a resource schedule is a (weakly non-decreasing) vector of length dmax that counts the number of channels available in the current period and next dmax - 1 periods given previous actions (C channels are available after this); an agent vector of size (k l) that provides a count of the number of agents present but not allocated for each possible per-unit value and each possible duration (the duration is automatically decremented when an agent remains in the system for a period without receiving an allocation); the time remaining until horizon T . Action space: The policy can postpone an agent allocation, or allocate an agent to a chan- nel for the remaining duration of the agent's time in the system if a channel is available, and the remaining duration is not greater than dmax. Payoff function: The reward at a time step is the summed value obtained from all agents for which an allocation is made in this time step. This is the total value such an agent will receive before it departs. Transition probabilities: The change in resource schedule, and in the agent vector that relates to agents currently present, is deterministic. The random new additions to the agent vector at each step are unaffected by the actions and also independent of time. Mechanisms. In the exact online VCG mechanism we compute an optimal policy, and optimal MDP values, offline using finite-horizon value iteration [7]. In the sparse- sampling( ) approach, we define a sampling tree depth L (perhaps < T ) and sample each state m times. This limited sampling depth places a lower-bound on the best possible ap- proximation accuracy from the sparse-sampling algorithm. We also employ agent pruning, with the agent vector in the state representation pruned to remove dominated agents: con- sider agent type with duration d and value v and remove all but C - N agents where N is the number of agents that either have remaining duration d and value > v or duration < d and value v. In computing payments we use factoring, and only determine VCG payments once for each type of agent to arrive. We compare performance with a simple fixed-price allocation scheme that given a particular problem, computes off-line a fixed number of periods and a fixed price (agents are queued and offered the price at random as resources become available) that yields the maximum expected total value. Results In the default model, we set C = 5, A = 5, define the set of values V = {1, 2, 3}, define the set of durations D = {1, 2, 6}, with lookahead L = 4 and sampling width m = 6. All results are averaged over at least 10 instances, and experiments were performed on a 3GHz P4, with 512 MB RAM. Value and revenue is normalized by the total value demanded by all agents, i.e. the value with infinite capacity.2 Looking first at economic properties, Figure 1(A) shows the effect of varying the number of agents from 2 to 12, comparing the value and revenue between the approximate online VCG mechanism and the fixed price mechanism. Notice that the MDP method dominates the price-based scheme for value, with a notable performance improvement over fixed price when demand is neither very low (no contention) nor very high (lots of competition). Revenue is also generally better from the MDP-based mechanism than in the fixed price scheme. Fig. 1(B) shows the similar effect of varying the number of channels from 3 to 10. Turning now to computational properties, Figure 1 (C) illustrates the effectiveness of sparse-sampling, and also agent pruning, sampled over 100 instances. The model is very 2This explains why the value appears to drop as we scale up the number of agents-- the total available value is increasing but supply remains fixed. 100 value:mdp value:mdp 80 rev:mdp rev:mdp value:fixed 80 value:fixed rev:fixed rev:fixed 60 60 % % 40 40 20 20 2 4 6 8 10 12 03 4 5 6 7 8 9 10 Number of agents Number of channels 98 1.0 600 value:pruning vs. #agents time:pruning vs. #agents (no pruning) 96 value:no pruning 0.8 500 time:no pruning vs. #channels 400 94 0.6 300 92 0.4 Run time (s) % of Exact Value % of Exact Time 200 90 0.2 time:pruning 100 time:no pruning 88 0 0 2 4 6 8 10 2 4 6 8 10 12 Sampling Width Number of Agents Figure 1: (A) Value and Revenue vs. Number of Agents. (B) Value and Revenue vs. Number of Channels. (C) Effect of Sampling Width. (D) Pruning speed-up. small: A = 2, C = 2, D = {1, 2, 3}, V = {1, 2, 3} and L = 4, to allow a compari- son with the compute time for an optimal policy. The sparse-sampling method is already running in less than 1% of the time for optimal value-iteration (right-hand axis), with an accuracy as high as 96% of the optimal. Pruning provides an incremental speed-up, and actually improves accuracy, presumably by making better use of each sample. Figure 1 (D) shows that pruning is extremely useful computationally (in comparison with plain sparse- sampling), for the default model parameters and as the number of agents is increased from 2 to 12. Pruning is effective, removing around 50% of agents (summed across all states in the lookahead tree) at 5 agents. Acknowledgments. David Parkes was funded by NSF grant IIS-0238147. Satinder Singh was funded by NSF grant CCF 0432027 and by a grant from DARPA's IPTO program.

It is useful to prove that an implementation correctly follows a specification. But even with a provably correct implementation, given a choice, would a node choose to follow it? This paper explores how to create distributed system specifications that will be faithfully implemented in networks with rational nodes, so that no node will choose to deviate. Given a strategyproof centralized mechanism, and given a network of nodes modeled as having rational-manipulation faults, we provide a proof technique to establish the incentive-, communication-, and algorithm-compatibility properties that guarantee that participating nodes are faithful to a suggested specification. As a case study, we apply our methods to extend the strategyproof interdomain routing mechanism proposed by Feigenbaum, Papadimitriou, Sami, and Shenker (FPSS) [7], defining a faithful implementation.

We study a limited-supply online auction problem, in which an auctioneer has k goods to sell and bidders arrive and depart dynamically. We suppose that agent valuations are drawn independently from some unknown distribution and construct an adaptive auction that is nevertheless value- andtime-strategy proof. For the k=1 problem we have a strategyproof variant on the classic secretary problem. We present a 4-competitive (e-competitive) strategyproof online algorithm with respect to offline Vickrey for revenue (efficiency). We also show (in a model that slightly generalizes the assumption of independent valuations) that no mechanism can be better than 3/2-competitive (2-competitive) for revenue (efficiency). Our general approach considers a learning phase followed by an accepting phase, and is careful to handle incentive issues for agents that span the two phases. We extend to the k›1 case, by deriving strategyproof mechanisms which are constant-competitive for revenue and efficiency. Finally, we present some strategyproof competitive algorithms for the case in which adversary uses a distribution known to the mechanism.

We consider the parallels between the preference elicitation problem in combinatorial auctions and the problem of learning an unknown function from learning theory. We show that learning algorithms can be used as a basis for preference elicitation algorithms. The resulting elicitation algorithms perform a polynomial number of queries. We also give conditions under which the resulting algorithms have polynomial communication. Our conversion procedure allows us to generate combinatorial auction protocols from learning algorithms for polynomials, monotone DNF, and linear-threshold functions. In particular, we obtain an algorithm that elicits XOR bids with polynomial communication.

Online mechanism design (MD) considers the problem of provid- ing incentives to implement desired system-wide outcomes in sys- tems with self-interested agents that arrive and depart dynami- cally. Agents can choose to misrepresent their arrival and depar- ture times, in addition to information about their value for di(cid:11)erent outcomes. We consider the problem of maximizing the total long- term value of the system despite the self-interest of agents. The online MD problem induces a Markov Decision Process (MDP), which when solved can be used to implement optimal policies in a truth-revealing Bayesian-Nash equilibrium.

We consider the problem of designing mechanisms for online problems in which agents arrive over time and truthfully announce their arrival. These problems are becoming extremely common in a wide variety of problems involving wireless networking and webserving. We show how the standard results of mechanism design can be modified to apply to this setting, provide conditions under which efficient and incentive compatible mechanisms exist and analyze several important online models including wireless networks and web serving.

We present an approximately-efficient and approximately-strategyproof auction mechanism for a single-good multi-unit allocation problem. The bidding language in our auctions allows marginal-decreasing piecewise constant curves. First, we develop a fully polynomial-time approximation scheme for the multi-unit allocation problem, which computes a (1+ε)≈ in worst-case time T = O(n3/ε), given n bids each with a constant number of pieces. Second, we embed this approximation scheme within a Vickrey-Clarke-Groves (VCG) mechanism and compute payments to n agents for an asymptotic cost of O(T log n). The maximal possible gain from manipulation to a bidder in the combined scheme is bounded by ε/(1+ε) V, where V is the total surplus in the efficient outcome.

We consider the problem of designing fast and strategyproof exchanges for dynamic resource allocation problems in distributed systems. The exchange is implemented as a sequence of auctions, with dynamically arriving requests from agents matched with each auction. Each auction is associated with some consignment of the resources from a single seller. We provide a simple Virtual Worlds (VW) construction, that extends a fast and strategyproof mechanism for a single auction to apply to this sequence-of-auctions setting. Rather than match each buyer with a single auction, the VW mechanism allows buyers to be considered for multiple auctions while retaining strategyproofness.

This paper introduces computation compatibility and communication compatibility as requirements for a distributed mechanism implementation. Just as payments are used to create incentive compatible mechanisms, some technique must be used to create computation/communication compatible mechanisms. This paper explores computation redundancy and communication redundancy as two such techniques. This paper uses interdomain routing as an example domain, and considers where redundancy can succeed and fail in addressing cheating with respect to computation and communication.

We consider the problem of minimizing preference elicitation in efficient multiattribute auctions, that support dynamic negotiation over non-price based attributes such as quality, time-of-delivery, and processor speed. We introduce asynchronous price-based multiattribute auctions, with proxy bidding agents that sit between the auctioneer and the participants. Empirical results demonstrate the preference elicitation savings that are provided with minimal price spaces, asynchronous updates, and proxy agents.

Standard auction mechanisms often break down in important e-commerce applications, where agents demand bundles of complementary resources, i.e. "I only want B if I also get A". This paper describes iBundle, an ascending-price auction that is guaranteed to compute optimal bundle allocations with agents that follow a best-response bidding strategy. The auction prices bundles directly and allows agents to place additive or exclusive-or bids over collections of bundles. Empirical results confirm that iBundle generates efficient allocations for hard resource allocation problems. Furthermore, we shoe that iBundle generates solutions without complete revelation (or computation) of agent preferences.