Maximum Nash Welfare and Other Stories About EFX

Amanatidis, Georgios; Birmpas, Georgios; Filos-Ratsikas, Aris; Hollender, Alexandros; Voudouris, Alexandros A.

doi:10.24963/ijcai.2020/4

Cited by 33 publications

(36 citation statements)

References 1 publication

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“…The difference is that we strengthen strategyproofness to group strategyproofness, but only establish EF1 (weaker than EFX) and do not establish Lorenz-dominance. We note that the EFX property is also established by Amanatidis et al [3]. We view these results as complementary to ours, and together, they establish that MNW tie is group strategyproof, EFX, PO, Lorenzdominating, and polynomial-time computable, making it even more compelling.…”

Section: Related Worksupporting

confidence: 86%

“…There are two popular definitions of EFX (see[3]); this result holds for the stronger one: an allocation is EFX if the envy that one agent has toward another can be eliminated by removing any good from the envied agent's bundle.…”

mentioning

confidence: 99%

“…There are two popular definitions of EFX[3]. The original definition by Caragiannis et al[16] asks that agent i not envy agent j after removal of any good from agent j's bundle that has positive value for agent i, whereas a latter definition omits the requirement of "positive value".…”

mentioning

confidence: 99%

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Fair Division with Binary Valuations: One Rule to Rule Them All

Halpern¹,

Procaccia²,

Psomas³

et al. 2020

Preprint

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We study fair allocation of indivisible goods among agents. Prior research focuses on additive agent preferences, which leads to an impossibility when seeking truthfulness, fairness, and efficiency. We show that when agents have binary additive preferences, a compelling rule -maximum Nash welfare (MNW) -provides all three guarantees. Specifically, we show that deterministic MNW with lexicographic tie-breaking is group strategyproof in addition to being envy-free up to one good and Pareto optimal. We also prove that fractional MNWknown to be group strategyproof, envy-free, and Pareto optimal -can be implemented as a distribution over deterministic MNW allocations, which are envy-free up to one good. Our work establishes maximum Nash welfare as the ultimate allocation rule in the realm of binary additive preferences.

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Section: Related Worksupporting

confidence: 86%

mentioning

confidence: 99%

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Fair Division with Binary Valuations: One Rule to Rule Them All

Halpern¹,

Procaccia²,

Psomas³

et al. 2020

Preprint

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show abstract

“…Maximizing the Nash social welfare is often seen as a middle ground between maximizing the sum of utilities to the agents, which is unfair to minorities (as we observed), and maximizing the minimum utility to any agent, which is considered too extreme [2]. The solution that maximizes the Nash social welfare has also been shown to satisfy many other fairness desiderata [4,5,6,7,8,9,10,11]; for further discussion on this, see Section 6.…”

Section: Introductionmentioning

confidence: 71%

Fair Algorithms for Multi-Agent Multi-Armed Bandits

Hossain,

Micha,

Shah

2020

Preprint

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We propose a multi-agent variant of the classical multi-armed bandit problem, in which there are N agents and K arms, and pulling an arm generates a (possibly different) stochastic reward to each agent. Unlike the classical multi-armed bandit problem, the goal is not to learn the "best arm", as each agent may perceive a different arm as best for her. Instead, we seek to learn a fair distribution over arms. Drawing on a long line of research in economics and computer science, we use the Nash social welfare as our notion of fairness. We design multi-agent variants of three classic multi-armed bandit algorithms, and show that they achieve sublinear regret, now measured in terms of the Nash social welfare.

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“…Clearly, if u is an additive utility function such that for each r k ∈ R, u(r k ) ∈ {0, 1}, then u is a buyer utility function. This type of function is known as binary utility function, see [14]. Thus, the buyer scenarios are a generalization of identical scenarios and a generalization of binary scenarios.…”

Section: Preliminariesmentioning

confidence: 99%

Beyond identical utilities: buyer utility functions and fair allocations

Camacho¹,

Fonseca-Delgado²,

Pérez³

et al. 2021

Preprint

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The problem of finding envy-free allocations of indivisible goods can not always be solved; therefore, it is common to study some relaxations such as envy-free up to one good (EF1). Another property of interest for efficiency of an allocation is the Pareto Optimality (PO). Under additive utility functions, it is possible to find allocations EF1 and PO using Nash social welfare. However, to find an allocation that maximizes the Nash social welfare is a computationally hard problem. In this work we propose a polynomial time algorithm which maximizes the utilitarian social welfare and at the same time produces an allocation which is EF1 and PO in a special case of additive utility functions called buyer utility functions. Moreover, a slight modification of our algorithm produces an allocation which is envy-free up to any positively valued good (EFX).

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Maximum Nash Welfare and Other Stories About EFX

Cited by 33 publications

References 1 publication

Fair Division with Binary Valuations: One Rule to Rule Them All

Fair Division with Binary Valuations: One Rule to Rule Them All

Fair Algorithms for Multi-Agent Multi-Armed Bandits

Beyond identical utilities: buyer utility functions and fair allocations

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