Fair allocation of indivisible goods has attracted extensive attention over the last two decades, yielding numerous elegant algorithmic results and producing challenging open questions. The problem becomes much harder in the presence of strategic agents. Ideally, one would want to design truthful mechanisms that produce allocations with fairness guarantees. However, in the standard setting without monetary transfers, it is generally impossible to have truthful mechanisms that provide non-trivial fairness guarantees. Recently, Amanatidis et al. [2021] suggested the study of mechanisms that produce fair allocations in their equilibria. Specifically, when the agents have additive valuation functions, the simple Round-Robin algorithm always has pure Nash equilibria and the corresponding allocations are envy-free up to one good (EF1) with respect to the agents' true valuation functions. Following this agenda, we show that this outstanding property of the Round-Robin mechanism extends much beyond the above default assumption of additivity. In particular, we prove that for agents with cancelable valuation functions (a natural class that contains, e.g., additive and budget-additive functions), this simple mechanism always has equilibria and even its approximate equilibria correspond to approximately EF1 allocations with respect to the agents' true valuation functions. Further, we show that the approximate EF1 fairness of approximate equilibria surprisingly holds for the important class of submodular valuation functions as well, even though exact equilibria fail to exist!

We consider the One-Sided Matching problem, where n agents have preferences over n items, and these preferences are induced by underlying cardinal valuation functions. The goal is to match every agent to a single item so as to maximize the social welfare. Most of the related literature, however, assumes that the values of the agents are not a priori known, and only access to the ordinal preferences of the agents over the items is provided. Consequently, this incomplete information leads to loss of efficiency, which is measured by the notion of distortion. In this paper, we further assume that the agents can answer a small number of queries, allowing us partial access to their values. We study the interplay between elicited cardinal information (measured by the number of queries per agent) and distortion for One-Sided Matching, as well as a wide range of well-studied related problems. Qualitatively, our results show that with a limited number of queries, it is possible to obtain significant improvements over the classic setting, where only access to ordinal information is given.

We consider the problem of fairly allocating a set of indivisible goods to a set of strategic agents with additive valuation functions. We assume no monetary transfers and, therefore, a mechanism in our setting is an algorithm that takes as input the reported -- rather than the true -- values of the agents. Our main goal is to explore whether there exist mechanisms that have pure Nash equilibria for every instance and, at the same time, provide fairness guarantees for the allocations that correspond to these equilibria. We focus on two relaxations of envy-freeness, namely envy-freeness up to one good (EF1), and envy-freeness up to any good (EFX), and we positively answer the above question. In particular, we study two algorithms that are known to produce such allocations in the non-strategic setting: Round-Robin (EF1 allocations for any number of agents) and a cut-and-choose algorithm of Plaut and Roughgarden [SIAM Journal of Discrete Mathematics, 2020] (EFX allocations for two agents). For Round-Robin we show that all of its pure Nash equilibria induce allocations that are EF1 with respect to the underlying true values, while for the algorithm of Plaut and Roughgarden we show that the corresponding allocations not only are EFX but also satisfy maximin share fairness, something that is not true for this algorithm in the non-strategic setting! Further, we show that a weaker version of the latter result holds for any mechanism for two agents that always has pure Nash equilibria which all induce EFX allocations.

Recent results in the ML community have revealed that learning algorithms used to compute the optimal strategy for the leader to commit to in a Stackelberg game, are susceptible to manipulation by the follower. Such a learning algorithm operates by querying the best responses or the payoffs of the follower, who consequently can deceive the algorithm by responding as if his payoffs were much different than what they actually are. For this strategic behavior to be successful, the main challenge faced by the follower is to pinpoint the payoffs that would make the learning algorithm compute a commitment so that best responding to it maximizes the follower's utility, according to his true payoffs. While this problem has been considered before, the related literature only focused on the simplified scenario in which the payoff space is finite, thus leaving the general version of the problem unanswered. In this paper, we fill in this gap, by showing that it is always possible for the follower to compute (near-)optimal payoffs for various scenarios about the learning interaction between leader and follower.