AI systems are increasingly used to support human decision-making. In many cases, despite the algorithm's superior performance, the final decision remains in human hands. For example, an AI may assist doctors in determining which diagnostic tests to run, but the doctor ultimately makes the diagnosis. Focusing on these scenarios, this paper studies AI-assisted decision-making where the human learns through repeated interactions with the algorithm. In our framework, the algorithm - designed to maximize decision accuracy according to its own model - determines which features the human can consider. The human then makes a prediction based on their own, less accurate model. Additionally, we consider the possibility of a constraint on the number of features that can be taken into account.

We devise a general graph-theoretic framework for studying prophet inequalities. In this framework, an agent traverses a directed acyclic graph from a starting node s to a target node t. Each edge has a value that is sampled from a known distribution. When the agent reaches a node υ it observes the realized values of all the outgoing edges from υ. The agent's objective is to maximize the expected total value of the path it takes. As in prophet inequalities, we compare the agent's performance against a prophet who observes all the realizations of the edges' values ahead of time. Our analysis reveals that this ratio highly depends on the number of paths k required to cover all the nodes in the graph. In particular, we provide an algorithm that guarantees a prophet inequality ratio of [EQUATION] and show an upper bound of [EQUATION].

A fundamental component in the growing theoretical literature on school choice is the problem a student faces in deciding which schools to apply to. Recent models have considered a setting with a set of schools of different selectiveness, and a student who is unsure of their strength as an applicant and can apply to at most k schools [Ali and Shorrer, 2023]. Such models assume that the student cares solely about maximizing the quality of the school that they will attend. However, experience suggests that students' decisions are additionally influenced by a set of crucial behavioral biases based on reputational effects: they experience a subjective reputational benefit when they are admitted to a selective school, whether or not they attend; and a subjective loss based on disappointment when they are rejected. Guided by these observations, and inspired by recent behavioral economics work on loss aversion relative to expectations [Dreyfuss et al., 2022, Kőszegi and Rabin, 2006, 2007, 2009, Meisner and von Wangenheim, 2023], we propose a behavioral model by which a student chooses schools in a way that balances these subjective behavioral effects with the quality of the school they eventually attend.

We study incentive-compatible mechanisms that maximize the Nash Social Welfare. Since traditional incentive-compatible mechanisms cannot maximize the Nash Social Welfare even approximately, we propose changing the traditional model. Inspired by a widely used charging method (e.g., royalties, a lawyer that charges some percentage of possible future compensation), we suggest charging the players some percentage of their value of the outcome. We call this model the percentage fee model. We show that there is a mechanism that maximizes exactly the Nash Social Welfare in every setting with non-negative valuations. Moreover, we prove an analog of Roberts theorem that essentially says that if the valuations are non-negative, then the only implementable social choice functions are those that maximize weighted variants of the Nash Social Welfare. We develop polynomial time incentive compatible approximation algorithms for the Nash Social Welfare with subadditive valuations and prove some hardness results. 26 pages. This is the TheoretiCS journal version

Organizational clusters are often shared among users who compete over resources, but the organization's goal is to increase the overall utility produced by the cluster. That is, to increase the aggregate benefit drawn from the cluster. To overcome this problem, we enhanced SLURM with an auctioning system. We evaluated our work on several real cluster traces. Our auctioning scheduler increases the responsiveness to highly valued jobs. It reduces the weight of the queued jobs (the sum of multiplication of jobs by their wait time by their number of required nodes and by their bid) by 3X--33X compared with backfilling.

We present a complete information game-theoretic model for crowdsourcing contests. We observe that in design contests, coding contests and other domains, separating low quality submissions from high quality ones is often easy. However, pinning down the best submission is more challenging since there is no objective measure. We model this situation by assuming that each contestant has an ability, which we interpret as its probability of submitting a high-quality submission. After the contestants decide whether or not they want to participate, the organizer of the contest needs to break ties between the high quality submissions. A common assumption in the literature is that the exact tie-breaking rule does not matter as long as ties are broken consistently. However, we show that the choice of the tie-breaking rule may have significant implications on the efficiency of the contest. Our results highlight both qualitative and quantitative differences between various deterministic tie-breaking rules. Perhaps counterintuitively, we show that in many scenarios, the utility of the organizer is maximized when ties are broken in favor of successful players with lower ability. Nevertheless, we show that the natural rule of choosing the submission of the successful player with the highest ability guarantees the organizer at least 1/3 of its utility under any tie-breaking rule. To complement these results, we provide an upper bound of Hn ~ \ln(n) on the price of anarchy (the ratio between the social welfare of the optimal solution and the social welfare of the Nash equilibrium). We show that this ratio is tight when ties are broken in favor of players with higher abilities.

A rapidly growing literature on lying in behavioral economics and psychology shows that individuals often do not lie even when lying maximizes their utility. In this work, we attempt to incorporate these findings into the theory of mechanism design. We consider players that have a preference for truth-telling and will only lie if their benefit from lying is sufficiently larger than the loss of the others. To accommodate such players, we introduce α-moral mechanisms, in which the gain of a player from misreporting his true value, comparing to truth-telling, is at most α times the loss that the others incur due to misreporting. Note that a 0-moral mechanism is a truthful mechanism. We develop a theory of moral mechanisms in the canonical setting of single-item auctions within the "reasonable" range of α, 0 ≤ α ≤ 1. We identify similarities and disparities to the standard theory of truthful mechanisms. In particular, we show that the allocation function does not uniquely determine the payments and is unlikely to admit a simple characterization. In contrast, recall that monotonicity characterizes the allocation function of truthful mechanisms. Our main technical effort is invested in determining whether the auctioneer can exploit the preference for truth-telling of the players to extract more revenue comparing to truthful mechanisms. We show that the auctioneer can indeed extract more revenue when the values of the players are correlated, even when there are only two players. However, we show that truthful mechanisms are revenue-maximizing even among moral ones when the values of the players are independently drawn from certain identical distributions (e.g., the uniform and exponential distributions). A by-product of our proof that optimal moral mechanisms are truthful is an alternative proof to Myerson’s optimal truthful mechanism characterization in the settings that we consider. We flesh out this approach by providing an alternative proof that does not involve moral mechanisms to Myerson’s characterization of optimal truthful mechanisms to all settings in which the values are independently drawn from regular distributions (not necessarily identical).

Organizational clusters are often shared among users who compete over resources, but the organization's goal is to increase the overall utility gathered from the cluster. That is, to maximize the aggregate benefit drawn from the cluster. To overcome this problem, we enhanced SLURM with an auctioning system. We evaluated our work on several real cluster traces. Our auctioning scheduler reduces the weight of the queued jobs by 3X-33X compared with backfilling.

One of the central human biases studied in behavioral economics is reference dependence - people's tendency to evaluate an outcome not in absolute terms but instead relative to a reference point that reflects some notion of the status quo [4]. Reference dependence interacts closely with a related behavioral bias, loss aversion, in which people weigh losses more strongly than gains of comparable absolute values. Taken together, these two effects produce a fundamental behavioral regularity in human choices: once a reference point has been established, people tend to avoid outcomes in which they experience a loss relative to the reference point. A well-known instance of the effect is the empirical evidence that individual investors will tend to avoid selling a stock unless it has exceeded the price at which they purchased it.

We present a novel model for capturing the behavior of an agent exhibiting sunk-cost bias in a stochastic environment. Agents exhibiting sunk-cost bias take into account the effort they have already spent on an endeavor when they evaluate whether to continue or abandon it. We model planning tasks in which an agent with this type of bias tries to reach a designated goal. Our model structures this problem as a type of Markov decision process: loosely speaking, the agent traverses a directed acyclic graph with probabilistic transitions, paying costs for its actions as it tries to reach a target node containing a specified reward. The agent’s sunk cost bias is modeled by a cost that it incurs for abandoning the traversal: if the agent decides to stop traversing the graph, it incurs a cost of $\lambda \cdot C_{sunk}$, where ${\lambda \geq 0}$ is a parameter that captures the extent of the bias and $C_{sunk}$ is the sum of costs already invested. We analyze the behavior of two types of agents: naive agents that are unaware of their bias, and sophisticated agents that are aware of it. Since optimal (bias-free) behavior in this problem can involve abandoning the traversal before reaching the goal, the bias exhibited by these types of agents can result in sub-optimal behavior by shifting their decisions about abandonment. We show that in contrast to optimal agents, it is computationally hard to compute the optimal policy for a sophisticated agent. Our main results quantify the loss exhibited by these two types of agents with respect to an optimal agent. We present both general and topology-specific bounds.

We study combinatorial auctions with bidders that exhibit endowment effect. In most of the previous work on cognitive biases in algorithmic game theory (e.g., [Kleinberg and Oren, EC'14] and its follow-ups) the focus was on analyzing the implications and mitigating their negative consequences. In contrast, in this paper we show how in some cases cognitive biases can be harnessed to obtain better outcomes. Specifically, we study Walrasian equilibria in combinatorial markets. It is well known that Walrasian equilibria exist only in limited settings, e.g., when all valuations are gross substitutes, but fails to exist in more general settings, e.g., when the valuations are submodular. We consider combinatorial settings in which bidders exhibit the endowment effect, that is, their value for items increases with ownership. Our main result shows that when the valuations are submodular, even a mild degree of endowment effect is sufficient to guarantee the existence of Walrasian equilibria. In fact, we show that in contrast to Walrasian equilibria with standard utility maximizing bidders -- in which the equilibrium allocation must be efficient -- when bidders exhibit endowment effect any local optimum can be an equilibrium allocation. Our techniques reveal interesting connections between the LP relaxation of combinatorial auctions and local maxima. We also provide lower bounds on the intensity of the endowment effect that the bidders must have in order to guarantee the existence of a Walrasian equilibrium in various settings.

Recent work has considered theoretical models for the behavior of agents with specific behavioral biases: rather than making decisions that optimize a given payoff function, the agent behaves inefficiently because its decisions suffer from an underlying bias. These approaches have generally considered an agent who experiences a single behavioral bias, studying the effect of this bias on the outcome. In general, however, decision-making can and will be affected by multiple biases operating at the same time. How do multiple biases interact to produce the overall outcome? Here we consider decisions in the presence of a pair of biases exhibiting an intuitively natural interaction: present bias -- the tendency to value costs incurred in the present too highly -- and sunk-cost bias -- the tendency to incorporate costs experienced in the past into one's plans for the future.

Exclusive social groups are ones in which the group members decide whether or not to admit a candidate to the group. Examples of exclusive social groups include academic departments and fraternal organizations. In the present paper we introduce an analytic framework for studying the dynamics of exclusive social groups. In our model, every group member is characterized by his opinion, which is represented as a point on the real line. The group evolves in discrete time steps through a voting process carried out by the group's members. Due to homophily, each member votes for the candidate who is more similar to him (i.e., closer to him on the line). An admission rule is then applied to determine which candidate, if any, is admitted. We consider several natural admission rules including majority and consensus.

Present bias, the tendency to weigh costs and benefits incurred in the present too heavily, is one of the most widespread human behavioral biases. It has also been the subject of extensive study in the behavioral economics literature. While the simplest models assume that decision-making agents are naive, reasoning about the future without taking their bias into account, there is considerable evidence that people often behave in ways that are sophisticated with respect to present bias, making plans based on the belief that they will be present-biased in the future. For example, committing to a course of action to reduce future opportunities for procrastination or overconsumption are instances of sophisticated behavior in everyday life.

A fundamental decision faced by a firm hiring employees --- and a familiar one to anyone who has dealt with the academic job market, for example --- is deciding what caliber of candidates to pursue. Should the firm try to increase its reputation by making offers to higher-quality candidates, despite the risk that the candidates might reject the offers and leave the firm empty-handed? Or is it better to play it safe and go for weaker candidates who are more likely to accept the offer? The question acquires an added level of complexity once we take into account the effect one hiring cycle has on the next: hiring better employees in the current cycle increases the firm's reputation, which in turn increases its attractiveness for higher-quality candidates in the next hiring cycle. These considerations introduce an interesting temporal dynamic aspect to the rich line of research on matching models for job markets, in which long-range planning and evolving reputational effects enter into the strategic decisions made by competing firms.

In many settings, people exhibit behavior that is inconsistent across time ' we allocate a block of time to get work done and then procrastinate, or put effort into a project and then later fail to complete it. An active line of research in behavioral economics and related fields has developed and analyzed models for this type of time-inconsistent behavior.

We study the necessity of interaction between individuals for obtaining approximately efficient economic allocations. We view this as a formalization of Hayek's classic point of view that focuses on the information transfer advantages that markets have relative to centralized planning. We study two settings: combinatorial auctions with unit demand bidders (bipartite matching) and combinatorial auctions with subadditive bidders. In both settings we prove that non-interactive protocols require exponentially larger communication costs than interactive ones, even those that only use a modest amount of interaction.

An active line of research has considered games played on networks in which payoffs depend on both a player's individual decision and also the decisions of his or her neighbors. Such games have been used to model issues including the formation of opinions (in which people wish to express views consistent with those of their friends) and technology adoption (in which people or firms seek compatibility with their network neighbors).

Human societies exhibit many forms of cultural diversity --- in the languages that are spoken, in the opinions and values that are held, and in many other dimensions. An active body of research in the mathematical social sciences has developed models for reasoning about the origins of this diversity, and about how it evolves over time.

Many large decentralized systems rely on information propagation to ensure their proper function. We examine a common scenario in which only participants that are aware of the information can compete for some reward, and thus informed participants have an incentive not to propagate information to others. One recent example in which such tension arises is the 2009 DARPA Network Challenge (finding red balloons). We focus on another prominent example: Bitcoin, a decentralized electronic currency system.

We study combinatorial procurement auctions, where a buyer with a valuation function v and budget B wishes to buy a set of items. Each item i has a cost ci and the buyer is interested in a set S that maximizes v(S) subject to ∑i∈Sci ≤ β. Special cases of combinatorial procurement auctions are well-studied problems from submodular optimization. In particular, when the costs are all equal (cardinality constraint), a classic result by Nemhauser et al shows that the greedy algorithm provides an e/e-1 approximation.

Coordination is a challenging everyday task; just think of the last time you organized a party or a meeting involving several people. As a growing part of our social and professional life goes online, an opportunity for an improved coordination process arises. Recently, Gupta et al. proposed entangled queries as a declarative abstraction for data-driven coordination, where the difficulty of the coordination task is shifted from the user to the database. Unfortunately, evaluating entangled queries is very hard, and thus previous work considered only a restricted class of queries that satisfy safety (the coordination partners are fixed) and uniqueness (all queries need to be satisfied). In this paper we significantly extend the class of feasible entangled queries beyond uniqueness and safety. First, we show that we can simply drop uniqueness and still efficiently evaluate a set of safe entangled queries. Second, we show that as long as all users coordinate on the same set of attributes, we can give an efficient algorithm for coordination even if the set of queries does not satisfy safety. In an experimental evaluation we show that our algorithms are feasible for a wide spectrum of coordination scenarios.

A long-standing line of work in economic theory has studied models by which a group of people in a social network, each holding a numerical opinion, can arrive at a shared opinion through repeated averaging with their neighbors in the network. Motivated by the observation that consensus is rarely reached in real opinion dynamics, we study a related sociological model in which individuals' intrinsic beliefs counterbalance the averaging process and yield a diversity of opinions. By interpreting the repeated averaging as best-response dynamics in an underlying game with natural payoffs, and the limit of the process as an equilibrium, we are able to study the cost of disagreement in these models relative to a social optimum. We provide a tight bound on the cost at equilibrium relative to the optimum, our analysis draws a connection between these agreement models and extremal problems for generalized eigenvalues. We also consider a natural network design problem in this setting, where adding links to the underlying network can reduce the cost of disagreement at equilibrium.

Scientific communities confer many forms of credit --- both implicit and explicit --- on their successful members, and it has long been argued that the motivation provided by these forms of credit helps to shape a community's collective attention toward different lines of research. The allocation of scientific credit, however, has also been the focus of long-documented pathologies: certain research questions are said to command too much credit, at the expense of other equally important questions; and certain researchers (in a version of Robert Merton's Matthew Effect) seem to receive a disproportionate share of the credit, even when the contributions of others are similar.