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Maximin Fair Allocation of Indivisible Items Under Cost Utilities

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Algorithmic Game Theory (SAGT 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14238))

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Abstract

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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Notes

  1. 1.

    Bansal and Sviridenko [7] call them restricted assignment valuations, while Camacho et al. [13] call them generalised binary valuations. Akrami et al. [1] study them under the name restricted additive valuations. We use the term “cost utilities” as we find it conceptually the most appealing and descriptive.

  2. 2.

    This is possible because we know that any good in the set is either approved by all three agents, or a subset of two. Agent 2 is a member of any subset of size two except \(A_{13}\).

  3. 3.

    We prove Proposition 1 for a picking sequence used in the proof of Proposition 2, but note that there are simpler picking sequences for which it holds.

  4. 4.

    This is under the assumption P\(\ne \)NP.

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Acknowledgements

This project was partially supported by the ARC Laureate Project FL200100204 on “Trustworthy AI”.

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Authors and Affiliations

  1. UNSW Sydney, Kensington, Australia

    Sirin Botan, Angus Ritossa, Mashbat Suzuki & Toby Walsh

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  1. Sirin Botan
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  2. Angus Ritossa
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  3. Mashbat Suzuki
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Correspondence to Mashbat Suzuki .

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Editors and Affiliations

  1. Royal Holloway University of London, Egham, UK

    Argyrios Deligkas

  2. University of Edinburgh, Edinburgh, UK

    Aris Filos-Ratsikas

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Botan, S., Ritossa, A., Suzuki, M., Walsh, T. (2023). Maximin Fair Allocation of Indivisible Items Under Cost Utilities. In: Deligkas, A., Filos-Ratsikas, A. (eds) Algorithmic Game Theory. SAGT 2023. Lecture Notes in Computer Science, vol 14238. Springer, Cham. https://doi.org/10.1007/978-3-031-43254-5_13

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  • DOI: https://doi.org/10.1007/978-3-031-43254-5_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-43253-8

  • Online ISBN: 978-3-031-43254-5

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