Fair Division of Indivisible Goods: A Survey

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

doi:10.48550/arxiv.2208.08782

Cited by 5 publications

(4 citation statements)

References 84 publications

(145 reference statements)

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“…The problem of fairly allocating indivisible goods to additive agents in the non-strategic setting has been extensively studied; for a recent survey, see Amanatidis et al [6]. Although the additivity of the valuation functions is considered a standard assumption, there are many works that explore richer classes of valuation functions.…”

Section: Further Related Workmentioning

confidence: 99%

“…In the last two decades fair allocation of indivisible items has attracted extensive attention, especially within the theoretical computer science community, yielding numerous elegant algorithmic results for various new fairness notions tailored to this discrete version of the problem, such as envy-freeness up to one good (EF1) [28,16], envy-freeness up to any good (EFX) [18], and maximin share fairness (MMS) [16]. We refer the interested reader to the surveys of Procaccia [34], Bouveret et al [15], Amanatidis et al [6].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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: Introductionmentioning

confidence: 99%

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

Amanatidis¹,

Birmpas²,

Lazos³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Therefore, the focus has been on finding approximate solutions, where in an α-MMS (APS) allocation, every agent receives a bundle worth at least α times their MMS (APS) value. This problem has been studied extensively for additive valuations (see (Amanatidis et al 2022) for a survey and pointers) with much progress (Procaccia and Wang 2014; Garg, McGlaughlin, and Taki 2018;Kulkarni, Mehta, and Taki 2021). It is known that a ( 3 4 + 3 3836 )-MMS always exists and can be computed in polynomial time , while there are examples showing that 39 40 -MMS may not exist (Feige, Sapir, and Tauber 2021) even in the setting of three agents.…”

Section: Introductionmentioning

confidence: 99%

1/2-Approximate MMS Allocation for Separable Piecewise Linear Concave Valuations

Chekuri,

Kulkarni,

Kulkarni

et al. 2024

AAAI

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We study fair distribution of a collection of m indivisible goods among a group of n agents, using the widely recognized fairness principles of Maximin Share (MMS) and Any Price Share (APS). These principles have undergone thorough investigation within the context of additive valuations. We explore these notions for valuations that extend beyond additivity. First, we study approximate MMS under the separable (piecewise-linear) concave (SPLC) valuations, an important class generalizing additive, where the best known factor was 1/3-MMS. We show that 1/2-MMS allocation exists and can be computed in polynomial time, significantly improving the state-of-the-art. We note that SPLC valuations introduce an elevated level of intricacy in contrast to additive. For instance, the MMS value of an agent can be as high as her value for the entire set of items. We use a relax-and-round paradigm that goes through competitive equilibrium and LP relaxation. Our result extends to give (symmetric) 1/2-APS, a stronger guarantee than MMS. APS is a stronger notion that generalizes MMS by allowing agents with arbitrary entitlements. We study the approximation of APS under submodular valuation functions. We design and analyze a simple greedy algorithm using concave extensions of submodular functions. We prove that the algorithm gives a 1/3-APS allocation which matches the best-known factor. Concave extensions are hard to compute in polynomial time and are, therefore, generally not used in approximation algorithms. Our approach shows a way to utilize it within analysis (while bypassing its computation), and hence might be of independent interest.

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“…Recent research focuses more on allocations of indivisible items (Lipton et al 2004;Budish 2011;Conitzer, Freeman, and Shah 2017;Bu et al 2022b;Amanatidis et al 2022;Li, Bei, and Yan 2022). Obviously, violation of fairness is unavoidable in some scenarios, e.g., when the number of items is less than the number of agents (in which case some agents will receive an empty set).…”

Section: Introductionmentioning

confidence: 99%

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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Fair Division of Indivisible Goods: A Survey

Cited by 5 publications

References 84 publications

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

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

1/2-Approximate MMS Allocation for Separable Piecewise Linear Concave Valuations

Fair Division with Prioritized Agents

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