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Home > Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 32

Groupwise Maximin Fair Allocation of Indivisible Goods

March 15, 2023

Authors

Siddharth Barman

Indian Institute of Science


Arpita Biswas

Indian Institute of Science


Sanath Krishnamurthy

Chennai Mathematical Institute


Yadati Narahari

Indian Institute of Science


Published:

2018-02-08

Proceedings:

Proceedings of the AAAI Conference on Artificial Intelligence, 32

Volume

Issue:

Thirty-Second AAAI Conference on Artificial Intelligence 2018

Track:

AAAI Technical Track: Game Theory and Economic Paradigms

Downloads:

Download PDF

Abstract:

We study the problem of allocating indivisible goods among n agents in a fair manner. For this problem, maximin share (MMS) is a well-studied solution concept which provides a fairness threshold. Specifically, maximin share is defined as the minimum utility that an agent can guarantee for herself when asked to partition the set of goods into n bundles such that the remaining (n-1) agents pick their bundles adversarially. An allocation is deemed to be fair if every agent gets a bundle whose valuation is at least her maximin share. Even though maximin shares provide a natural benchmark for fairness, it has its own drawbacks and, in particular, it is not sufficient to rule out unsatisfactory allocations. Motivated by these considerations, in this work we define a stronger notion of fairness, called groupwise maximin share guarantee (GMMS). In GMMS, we require that the maximin share guarantee is achieved not just with respect to the grand bundle, but also among all the subgroups of agents. Hence, this solution concept strengthens MMS and provides an ex-post fairness guarantee. We show that in specific settings, GMMS allocations always exist. We also establish the existence of approximate GMMS allocations under additive valuations, and develop a polynomial-time algorithm to find such allocations. Moreover, we establish a scale of fairness wherein we show that GMMS implies approximate envy freeness. Finally, we empirically demonstrate the existence of GMMS allocations in a large set of randomly generated instances. For the same set of instances, we additionally show that our algorithm achieves an approximation factor better than the established, worst-case bound.

DOI:

10.1609/aaai.v32i1.11463


AAAI

Thirty-Second AAAI Conference on Artificial Intelligence 2018


ISSN 2374-3468 (Online) ISSN 2159-5399 (Print)


Published by AAAI Press, Palo Alto, California USA Copyright © 2018, Association for the Advancement of Artificial Intelligence All Rights Reserved.

Topics: AAAI

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