Welfare maximization in bilateral trade has been extensively studied in recent years. Previous literature obtained incentive-compatible approximation mechanisms only for the private values case. In this paper, we study welfare maximization in bilateral trade with interdependent values. Designing mechanisms for interdependent settings is much more challenging because the values of the players depend on the private information of the others, requiring complex belief updates and strategic inference.

We study truthful mechanisms for approximating the Maximin-Share (MMS) allocation of agents with additive valuations for indivisible goods. Algorithmically, constant factor approximations exist for the problem for any number of agents. When adding incentives to the mix, a jarring result by Amanatidis, Birmpas, Christodoulou, and Markakis [EC 2017] shows that the best possible approximation for two agents and $m$ items is $\lfloor \frac{m}{2} \rfloor$. We adopt a learning-augmented framework to investigate what is possible when some prediction on the input is given. For two agents, we give a truthful mechanism that takes agents' ordering over items as prediction. When the prediction is accurate, we give a $2$-approximation to the MMS (consistency), and when the prediction is off, we still get an $\lceil \frac{m}{2} \rceil$-approximation to the MMS (robustness). We further show that the mechanism's performance degrades gracefully in the number of ``mistakes" in the prediction; i.e., we interpolate (up to constant factors) between the two extremes: when there are no mistakes, and when there is a maximum number of mistakes. We also show an impossibility result on the obtainable consistency for mechanisms with finite robustness. For the general case of $n\ge 2$ agents, we give a 2-approximation mechanism for accurate predictions, with relaxed fallback guarantees. Finally, we give experimental results which illustrate when different components of our framework, made to insure consistency and robustness, come into play.

We study auction design within the widely acclaimed model of interdependent values, introduced by Milgrom and Weber [1982]. In this model, every bidder i has a private signal si for the item for sale, and a public valuation function υi (s1, ..., sn) which maps every vector of private signals (of all bidders) into a real value. A recent line of work established the existence of approximately-optimal mechanisms within this framework, even in the more challenging scenario where each bidder's valuation function υi is also private. This body of work has primarily focused on single-item auctions with two natural classes of valuations: those exhibiting submodularity over signals (SOS) and d-critical valuations.

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 celebrated model of auctions with interdependent valuations, introduced by Milgrom and Weber in 1982, has been studied almost exclusively under private signals $s_{1}, \ldots, s_{n}$ of the n bidders and public valuation functions $v_{i}\left(s_{1}, \ldots, s_{n}\right)$. Recent work in TCS has shown that this setting admits a constant approximation to the optimal social welfare if the valuations satisfy a natural property called submodularity over signals (SOS). More recently, Eden et al. (2022) have extended the analysis of interdependent valuations to include settings with private signals and private valuations, and established $O\left(\log ^{2} n\right)$-approximation for SOS valuations. In this paper we show that this setting admits a constant factor approximation, settling the open question raised by Eden et al. (2022).

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.

In real life auctions, a widely observed phenomenon is the winner's curse -- the winner's high bid implies that the winner often over-estimates the value of the good for sale, resulting in an incurred negative utility. The seminal work of Eyster and Rabin [Econometrica'05] introduced a behavioral model aimed to explain this observed anomaly. We term agents who display this bias "cursed agents". We adopt their model in the interdependent value setting, and aim to devise mechanisms that prevent the cursed agents from obtaining negative utility. We design mechanisms that are cursed ex-post IC, that is, incentivize agents to bid their true signal even though they are cursed, while ensuring that the outcome is individually rational -- the price the agents pay is no more than the agents' true value. Since the agents might over-estimate the good's value, such mechanisms might require the seller to make positive transfers to the agents to prevent agents from over-paying. For revenue maximization, we give the optimal deterministic and anonymous mechanism. For welfare maximization, we require ex-post budget balance (EPBB), as positive transfers might lead to negative revenue. We propose a masking operation that takes any deterministic mechanism, and imposes that the seller would not make positive transfers, enforcing EPBB. We show that in typical settings, EPBB implies that the mechanism cannot make any positive transfers, implying that applying the masking operation on the fully efficient mechanism results in a socially optimal EPBB mechanism. This further implies that if the valuation function is the maximum of agents' signals, the optimal EPBB mechanism obtains zero welfare. In contrast, we show that for sum-concave valuations, which include weighted-sum valuations and l_p-norms, the welfare optimal EPBB mechanism obtains half of the optimal welfare as the number of agents grows large.

We consider the single-item interdependent value setting, where there is a single item sold by a monopolist, n buyers, and each buyer has a private signal si describing a piece of information about the item. Additionally, each bidder i has a valuation function vi(s1, …, sn) mapping the (private) signals of all buyers into a positive real number representing their value for the item. This setting captures scenarios where the item's information is asymmetric or dispersed among agents, such as in competitions for oil drilling rights, or in auctions for art pieces. Due to the increased complexity of this model compared to the standard private values model, it is generally assumed that each bidder's valuation function vi is public knowledge to the seller or all other buyers. But in many situations, the seller may not know the bidders' valuation functions—how a bidder aggregates signals into a valuation is often their private information. In this paper, we design mechanisms that guarantee approximately-optimal social welfare while satisfying ex-post incentive compatibility and individually rationality for the case where the valuation functions are private to the bidders, and thus may be strategically misreported to the seller. When the valuations are public, it is possible for optimal social welfare to be attained by a deterministic mechanism when the valuations satisfy a single-crossing condition. In contrast, when the valuations are the bidders' private information, we show that no finite bound on the social welfare can be achieved by any deterministic mechanism even under single-crossing. Moreover, no randomized mechanism can guarantee better than n-approximation. We thus consider valuation functions that are submodular over signals (SOS), introduced in the context of combinatorial auctions in a recent breakthrough paper by Eden et al. [EC'19]. Our main result is an O(log2 n)-approximation randomized mechanism for buyers with private signals and valuations under the SOS condition. We also give a tight Θ(k)-approximation mechanism for the case each agent's valuation depends on at most k other signals even for unknown k.

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.

We expand the literature on the price of anarchy (PoA) of simultaneous item auctions by considering settings with correlated values; we do this via the fundamental economic model of interdependent values (IDV). It is well-known that in multi-item settings with private values, correlated values can lead to bad PoA, which can be polynomially large in the number of agents~n. In the more general model of IDV, we show that the PoA can be polynomially large even in single-item settings. On the positive side, we identify a natural condition on information dispersion in the market, which enables good PoA guarantees. Under this condition, we show that for single-item settings, the PoA of standard mechanisms degrades gracefully. For settings with multiple items we show a separation between two domains: If there are more buyers, we devise a new simultaneous item auction with good PoA, under limited information asymmetry. To the best of our knowledge, this is the first positive PoA result for correlated values in multi-item settings. The main technical difficulty in establishing this result is that the standard tool for establishing PoA results --- the smoothness framework --- is unsuitable for IDV settings, and so we must introduce new techniques to address the unique challenges imposed by such settings. In the domain of more items, we establish impossibility results even for surprisingly simple scenarios.

In this paper we consider the k-server problem where events are generated by selfish agents, known as the selfish k-server problem. In this setting, there is a set of k servers located in some metric space. Selfish agents arrive in an online fashion, each has a request located on some point in the metric space, and seeks to serve his request with the server of minimum distance to the request. If agents choose to serve their request with the nearest server, this mimics the greedy algorithm which has an unbounded competitive ratio. We propose an algorithm that associates a surcharge with each server independently of the agent to arrive (and therefore, yields a truthful online mechanism). An agent chooses to serve his request with the server that minimizes the distance to the request plus the associated surcharge to the server. This paper extends [Ilan Reuven Cohen et al., 2015], which gave an optimal k-competitive dynamic pricing scheme for the selfish k-server problem on the line. We give a k-competitive dynamic pricing algorithm for the selfish k-server problem on tree metric spaces, which matches the optimal online (non truthful) algorithm. We show that an alpha-competitive dynamic pricing scheme exists on the tree if and only if there exists alpha-competitive online algorithm on the tree that is lazy and monotone. Given this characterization, the main technical difficulty is coming up with such an online algorithm.

We give a prompt online mechanism for minimizing the sum of [weighted] completion times. This is the first prompt online algorithm for the problem. When such jobs are strategic agents, delaying scheduling decisions makes little sense. Moreover, the mechanism has a particularly simple form of an anonymous menu of options.

We consider a setting where an auctioneer sells a single item to n potential agents with interdependent values. That is, each agent has her own private signal, and the valuation of each agent is a known function of all n private signals. This captures settings such as valuations for oil drilling rights, broadcast rights, pieces of art, and many more.

Recent literature on approximately optimal revenue maximization has shown that in settings where agent valuations for items are complement free, the better of selling the items separately and bundling them together guarantees a constant fraction of the optimal revenue. However, most real-world settings involve some degree of complementarity among items. The role that complementarity plays in the trade-off of simplicity versus optimality has been an obvious missing piece of the puzzle. In “A Simple and Approximately Optimal Mechanism for a Buyer with Complements,” the authors show that the same simple selling mechanism—the better of selling separately and as a grand bundle—guarantees a $\Theta(d)$ fraction of the optimal revenue, where $d$ is a measure of the degree of complementarity. One key modeling contribution is a tractable notion of “degree of complementarity” that admits meaningful results and insights—they demonstrate that previous definitions fall short in this regard.

A seminal result of Bulow and Klemperer [1989] demonstrates the power of competition for extracting revenue: when selling a single item to n bidders whose values are drawn i.i.d. from a regular distribution, the simple welfare-maximizing VCG mechanism (in this case, a second price-auction) with one additional bidder extracts at least as much revenue in expectation as the optimal mechanism. The beauty of this theorem stems from the fact that VCG is a prior-independent mechanism, where the seller possesses no information about the distribution, and yet, by recruiting one additional bidder it performs better than any prior-dependent mechanism tailored exactly to the distribution at hand (without the additional bidder).

Walrasian prices, if they exist, have the property that one can assign every buyer some bundle in her demand set, such that the resulting assignment will maximize social welfare. Unfortunately, this assumes carefully breaking ties amongst different bundles in the buyer demand set. Presumably, the shopkeeper cleverly convinces the buyer to break ties in a manner consistent with maximizing social welfare. Lacking such a shopkeeper, if buyers arrive sequentially and simply choose some arbitrary bundle in their demand set, the social welfare may be arbitrarily bad. In the context of matching markets, we show how to compute dynamic prices, based upon the current inventory, that guarantee that social welfare is maximized. Such prices are set without knowing the identity of the next buyer to arrive. We also show that this is impossible in general (e.g., for coverage valuations), but consider other scenarios where this can be done. We further extend our results to Bayesian and bounded rationality models.

We extend the notion of Combinatorial Walrasian Equilibrium, as defined by \citet{FGL13}, to settings with budgets. When agents have budgets, the maximum social welfare as traditionally defined is not a suitable benchmark since it is overly optimistic. This motivated the liquid welfare of \cite{DP14} as an alternative. Observing that no combinatorial Walrasian equilibrium guarantees a non-zero fraction of the maximum liquid welfare in the absence of randomization, we instead work with randomized allocations and extend the notions of liquid welfare and Combinatorial Walrasian Equilibrium accordingly. Our generalization of the Combinatorial Walrasian Equilibrium prices lotteries over bundles of items rather than bundles, and we term it a lottery pricing equilibrium.

We consider dynamic pricing schemes in online settings where selfish agents generate online events. Previous work on online mechanisms has dealt almost entirely with the goal of maximizing social welfare or revenue in an auction settings. This paper deals with quite general settings and minimizing social costs. We show that appropriately computed posted prices allow one to achieve essentially the same performance as the best online algorithm. This holds in a wide variety of settings. Unlike online algorithms that learn about the event, and then make enforcable decisions, prices are posted without knowing the future events or even the current event, and are thus inherently dominant strategy incentive compatible. In particular we show that one can give efficient posted price mechanisms for metrical task systems, some instances of the k-server problem, and metrical matching problems. We give both deterministic and randomized algorithms. Such posted price mechanisms decrease the social cost dramatically over selfish behavior where no decision incurs a charge. One alluring application of this is reducing the social cost of free parking exponentially.