Fair and Efficient Allocations under Subadditive Valuations

Bhaskar Ray Chaudhury, Jugal Garg, Ruta Mehta

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We study the problem of allocating a set of indivisible goods among agents with subadditive valuations in a fair and efficient manner. Envy-Freeness up to any good (EFX) is the most compelling notion of fairness in the context of indivisible goods. Although the existence of EFX is not known beyond the simple case of two agents with subadditive valuations, some good approximations of EFX are known to exist, namely 12 -EFX allocation and EFX allocations with bounded charity. Nash welfare (the geometric mean of agents’ valuations) is one of the most commonly used measures of efficiency. In case of additive valuations, an allocation that maximizes Nash welfare also satisfies fairness properties like Envy-Free up to one good (EF1). Although there is substantial work on approximating Nash welfare when agents have additive valuations, very little is known when agents have subadditive valuations. In this paper, we design a polynomial-time algorithm that outputs an allocation that satisfies either of the two approximations of EFX as well as achieves an O(n) approximation to the Nash welfare. Our result also improves the current best-known approximation of O(n log n) and O(m) to Nash welfare when agents have submodular and subadditive valuations, respectively. Furthermore, our technique also gives an O(n) approximation to a family of welfare measures, p-mean of valuations for p ? (-8, 1], thereby also matching asymptotically the current best approximation ratio for special cases like p = -8 while also retaining the remarkable fairness properties.

Original languageEnglish (US)
Title of host publication35th AAAI Conference on Artificial Intelligence, AAAI 2021
PublisherAssociation for the Advancement of Artificial Intelligence
Number of pages8
ISBN (Electronic)9781713835974
StatePublished - 2021
Event35th AAAI Conference on Artificial Intelligence, AAAI 2021 - Virtual, Online
Duration: Feb 2 2021Feb 9 2021

Publication series

Name35th AAAI Conference on Artificial Intelligence, AAAI 2021


Conference35th AAAI Conference on Artificial Intelligence, AAAI 2021
CityVirtual, Online

ASJC Scopus subject areas

  • Artificial Intelligence


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