Generalized binary utility functions and fair allocations

Camacho, Franklin; Fonseca-Delgado, Rigoberto; Pérez, Ramón Pino; Tapia, Guido

doi:10.1016/j.mathsocsci.2022.10.003

Cited by 4 publications

(2 citation statements)

References 13 publications

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“…[50] proved that EF1+fPO allocation always exists in the case of three agents and at most two binary disutility functions, where fPO requires PO in all fractional results. In the generalized binary disutility (a disutility function d i is generalized binary if, for ∀i ∈ N, j ∈ C, d i (j) ∈ {0, 1} and d i is an additive disutility function) scenario of chores, the algorithm of Camacho et al (2023) [51] can give the allocation of EF1+PO in polynomial time O(mn). The problem discussed by Barman et al (2023) [52] is the fair allocation of indivisible chores under binary supermodular disuility functions.…”

Section: Example 1 ([45]mentioning

confidence: 99%

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A Survey on Fair Allocation of Chores

Guo,

Li,

Deng

2023

Mathematics

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Wherever there is group life, there has been a social division of labor and resource allocation, since ancient times. Examples include ant colonies, bee colonies, and wolf colonies. Different roles are responsible for different tasks. The same is true of human beings. Human beings are the largest social group in nature, among whom there are intricate social networks and interest networks between individuals. In such a complex relationship, how do decision makers allocate resources or tasks to individuals in a fair way? This is a topic worthy of further study. In recent decades, fair allocation has been at the core of research in economics, mathematics and other fields. The fair allocation problem is to assign a set of items to a set of agents so that each agent’s allocation is as fair as possible to satisfy each agent. The fairness measurements followed in current research include envy-freeness, proportionality, equitability, maximin share fairness, competitive equilibrium, maximum Nash social diswelfare, and so on. In this paper, the main concern is the allocation of chores. We discuss this problem in two parts: divisible and indivisible. We comprehensively review the existing results, algorithms, and approximations that meet various fairness criteria in chronological order. The relevant results of achieving fairness and efficiency are also discussed. In addition, we propose some open questions and future research directions for this problem based on existing research.

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Section: Example 1 ([45]mentioning

confidence: 99%

“…In the generalized binary disutility scenario of chores, the algorithm of [50] proved that EFX+fPO allocation always exists for three agents with bivalue disutility. Camacho et al (2023) [51] can give the EFX+PO allocation in O(mlogm + mn) time.…”

Section: Envy-free Up To Any Chorementioning

confidence: 99%

A Survey on Fair Allocation of Chores

Guo,

Li,

Deng

2023

Mathematics

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Maximin Fair Allocation of Indivisible Items Under Cost Utilities

Botan,

Ritossa,

Suzuki

et al. 2023

Lecture Notes in Computer Science

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We study the problem of fairly allocating indivisible goods among a set of agents. Our focus is on the existence of allocations that give each agent their maximin fair share-the value they are guaranteed if they divide the goods into as many bundles as there are agents, and receive their lowest valued bundle. An MMS allocation is one where every agent receives at least their maximin fair share. We examine the existence of such allocations when agents have cost utilities. In this setting, each item has an associated cost, and an agent's valuation for an item is the cost of the item if it is useful to them, and zero otherwise. Our main results indicate that cost utilities are a promising restriction for achieving MMS. We show that for the case of three agents with cost utilities, an MMS allocation always exists. We also show that when preferences are restricted slightly further-to what we call laminar set approvals-we can guarantee MMS allocations for any number of agents. Finally, we explore if it is possible to guarantee each agent their maximin fair share while using a strategyproof mechanism.

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Weighted fair division with matroid-rank valuations: Monotonicity and strategyproofness

Suksompong,

Teh

2023

Mathematical Social Sciences

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Generalized binary utility functions and fair allocations

Cited by 4 publications

References 13 publications

A Survey on Fair Allocation of Chores

A Survey on Fair Allocation of Chores

Maximin Fair Allocation of Indivisible Items Under Cost Utilities

Weighted fair division with matroid-rank valuations: Monotonicity and strategyproofness

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