Almost Full EFX Exists for Four Agents

Berger, Ben; Cohen, Avi; Feldman, Michal; Fiat, Amos

doi:10.1609/aaai.v36i5.20410

Cited by 27 publications

(14 citation statements)

References 9 publications

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“…ere are, however, positive results for any number of agents if the valuation functions are restricted [6,38,29], if it is allowed to discard some of the goods [19,22,23,12], or if one considers approximate EFX allocations [5]. Finally, regarding the notion of MMS, allocations that provide this guarantee always exist when there are only 2 agents, although computing them is an NP-hard problem [46].…”

Section: Further Related Workmentioning

confidence: 99%

Allocating Indivisible Goods to Strategic Agents: Pure Nash Equilibria and Fairness

Amanatidis

Birmpas

Fusco

et al. 2022

Web and Internet Economics

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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 se ing 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 se ing: Round-Robin (EF1 allocations for any number of agents) and a cut-and-choose algorithm of Plaut and Roughgarden [42] (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 se ing! Further, we show that a weaker version of the la er result holds for any mechanism for two agents that always has pure Nash equilibria which all induce EFX allocations. * is work was supported by the ERC Advanced Grant 788893 AMDROMA "Algorithmic and Mechanism Design Research in Online Markets", the MIUR PRIN project ALGADIMAR "Algorithms, Games, and Digital Markets", and the NWO Veni project No. VI.Veni.192.153.

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Section: Further Related Workmentioning

confidence: 99%

Allocating Indivisible Goods to Strategic Agents: Pure Nash Equilibria and Fairness

Amanatidis

Birmpas

Fusco

et al. 2022

Web and Internet Economics

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“…Chaudhury et al [2021c] presented an algorithm that computes a partial EFX allocation, but the number of unallocated goods is at most n−1, and no agent prefers the set of these goods to her own bundle. e la er result was recently improved by Berger et al [2022] who showed that the unallocated goods can be decreased to n − 2 in general, and to just one for the case of four agents. Finally, Chaudhury et al [2021b] showed that a (1 − ε)-EFX allocation with a sublinear number of unallocated goods and high Nash welfare can be computed in polynomial time for every constant ǫ ∈ (0, 0.5].…”

Section: Relaxations Of Efxmentioning

confidence: 99%

Fair Division of Indivisible Goods: A Survey

Amanatidis¹,

Birmpas²,

Filos-Ratsikas³

et al. 2022

Preprint

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Allocating resources to individuals in a fair manner has been a topic of interest since ancient times, with most of the early mathematical work on the problem focusing on resources that are infinitely divisible. Over the last decade, there has been a surge of papers studying computational questions regarding the indivisible case, for which exact fairness notions such as envy-freeness and proportionality are hard to satisfy. One main theme in the recent research agenda is to investigate the extent to which their relaxations, like maximin share fairness (MMS) and envy-freeness up to any good (EFX), can be achieved. In this survey, we present a comprehensive review of the progress made in the related literature by highlighting different ways to relax fairness notions, common algorithm design techniques, and the most interesting questions for future research.

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“…Although the additivity of the valuation functions is considered a standard assumption, there are many works that explore richer classes of valuation functions. Some prominent examples include the computation of EF1 allocations for agents with general non-decreasing valuation functions [28], EFX allocations (or relaxations of EFX) under agents with cancelable valuation functions [12,1,19] and subaditive valuation functions [33,20], respectively, and approximate MMS allocations for submodular, XOS, and subadditive agents [11,23].…”

Section: Further Related Workmentioning

confidence: 99%

“…Although the stability and equilibrium fairness properties of Round-Robin have been visited before [8,5], to the best of our knowledge, we are the first to study the problem for non-additive valuation functions and go beyond exact pure Nash equilibria. Cancelable functions also generalize budget-additive, unit-demand, and multiplicative valuation functions [12], and recently have been of interest in the fair division literature as several results can be extended to this class [12,1,19]. For similar reasons, cancelable functions seem to be a good pairing with Round-Robin as well, at least in the algorithmic setting (see, e.g., Proposition 2.5).…”

Section: Introductionmentioning

confidence: 97%

Round-Robin Beyond Additive Agents: Existence and Fairness of Approximate Equilibria

Amanatidis¹,

Birmpas²,

Lazos³

et al. 2023

Preprint

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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. [5] 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!

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Almost Full EFX Exists for Four Agents

Cited by 27 publications

References 9 publications

Allocating Indivisible Goods to Strategic Agents: Pure Nash Equilibria and Fairness

Allocating Indivisible Goods to Strategic Agents: Pure Nash Equilibria and Fairness

Fair Division of Indivisible Goods: A Survey

Round-Robin Beyond Additive Agents: Existence and Fairness of Approximate Equilibria

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