EFX Allocations: Simplifications and Improvements

Akrami, Hannaneh; Chaudhury, Bhaskar Ray; Garg, Jugal; Mehlhorn, Kurt; Mehta, Ruta

doi:10.48550/arxiv.2205.07638

Cited by 3 publications

(11 citation statements)

References 11 publications

(23 reference statements)

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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%

“…Formally, the preference ranking ≻ , which agent reports, defines a total order on , i.e., ≻ ′ implies that good precedes good ′ in agent ' declared preference ranking. 1 We call the vector of the agents' declared preference rankings, ≻ = (≻ 1 , . .…”

Section: Preliminariesmentioning

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%

“…The main result of this section is Theorem 3.7 stating that the bluff profile is a 1 2 -approximate PNE when agents have submodular valuation functions. While this sounds weaker than Theorem 3.2, it should be noted that for submodular agents Mechanism 1 does not have PNE in general, even for relatively simple instances, as stated in Proposition 3.4.…”

mentioning

confidence: 99%

“…Theorem 3.7. When all agents have submodular valuation functions, the bluff profile is a 1 2 -approximate PNE of Mechanism 1. Moreover, this is tight, i.e., for any > 0, there are instances where the bluff profile is not a 1 2 + -approximate PNE.…”

mentioning

confidence: 99%

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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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Section: Further Related Workmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

mentioning

confidence: 99%

mentioning

confidence: 99%

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

Amanatidis¹,

Birmpas²,

Lazos³

et al. 2023

Preprint

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

Amanatidis

Birmpas

Lazos³

et al. 2023

Proceedings of the 24th ACM Conference on Economics and Computation

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Constrained maximization of submodular functions poses a central problem in combinatorial optimization. In many realistic scenarios, a number of agents need to maximize multiple submodular objectives over the same ground set. We study such a se ing, where the different solutions must be disjoint, and thus, questions of fairness arise. Inspired from the fair division literature, we suggest a simple round-robin protocol, where agents are allowed to build their solutions one item at a time by taking turns. Unlike what is typical in fair division, however, the prime goal here is to provide a fair algorithmic environment; each agent is allowed to use any algorithm for constructing their respective solutions. We show that just by following simple greedy policies, agents have solid guarantees for both monotone and non-monotone objectives, and for combinatorial constraints as general as p-systems (which capture cardinality and matroid intersection constraints). In the monotone case, our results include approximate EF1-type guarantees and their implications in fair division may be of independent interest. Further, although following a greedy policy may not be optimal in general, we show that consistently performing be er than that is computationally hard.

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Fair Division with Prioritized Agents

Liu

et al. 2023

AAAI

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We consider the fair division problem of indivisible items. It is well-known that an envy-free allocation may not exist, and a relaxed version of envy-freeness, envy-freeness up to one item (EF1), has been widely considered. In an EF1 allocation, an agent may envy others' allocated shares, but only up to one item. In many applications, we may wish to specify a subset of prioritized agents where strict envy-freeness needs to be guaranteed from these agents to the remaining agents, while ensuring the whole allocation is still EF1. Prioritized agents may be those agents who are envious in a previous EF1 allocation, those agents who belong to underrepresented groups, etc. Motivated by this, we propose a new fairness notion named envy-freeness with prioritized agents EFprior, and study the existence and the algorithmic aspects for the problem of computing an EFprior allocation. With additive valuations, the simple round-robin algorithm is able to compute an EFprior allocation. In this paper, we mainly focus on general valuations. In particular, we present a polynomial-time algorithm that outputs an EFprior allocation with most of the items allocated. When all the items need to be allocated, we also present polynomial-time algorithms for some well-motivated special cases.

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EFX Allocations: Simplifications and Improvements

Cited by 3 publications

References 11 publications

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

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

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

Fair Division with Prioritized Agents

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