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Approximate maximin shares for groups of agents

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  • Suksompong, Warut

Abstract

We investigate the problem of fairly allocating indivisible goods among interested agents using the concept of maximin share. Procaccia and Wang showed that while an allocation that gives every agent at least her maximin share does not necessarily exist, one that gives every agent at least 2∕3 of her share always does. In this paper, we consider the more general setting where we allocate the goods to groups of agents. The agents in each group share the same set of goods even though they may have conflicting preferences. For two groups, we characterize the cardinality of the groups for which a positive approximation of the maximin share is possible regardless of the number of goods. We also show settings where an approximation is possible or impossible when there are several groups.

Suggested Citation

  • Suksompong, Warut, 2018. "Approximate maximin shares for groups of agents," Mathematical Social Sciences, Elsevier, vol. 92(C), pages 40-47.
    • Handle: RePEc:eee:matsoc:v:92:y:2018:i:c:p:40-47
    DOI: 10.1016/j.mathsocsci.2017.09.004
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    References listed on IDEAS

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    1. Steven Brams & D. Kilgour & Christian Klamler, 2012. "The undercut procedure: an algorithm for the envy-free division of indivisible items," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 615-631, July.
    2. Steven J. Brams & Peter C. Fishburn, 2000. "Fair division of indivisible items between two people with identical preferences: Envy-freeness, Pareto-optimality, and equity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(2), pages 247-267.
    3. Varian, Hal R., 1974. "Equity, envy, and efficiency," Journal of Economic Theory, Elsevier, vol. 9(1), pages 63-91, September.
    4. Moulin, Herve, 1990. "Uniform externalities : Two axioms for fair allocation," Journal of Public Economics, Elsevier, vol. 43(3), pages 305-326, December.
    5. Manurangsi, Pasin & Suksompong, Warut, 2017. "Asymptotic existence of fair divisions for groups," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 100-108.
    6. Eric Budish, 2011. "The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1061-1103.
    7. Suksompong, Warut, 2016. "Asymptotic existence of proportionally fair allocations," Mathematical Social Sciences, Elsevier, vol. 81(C), pages 62-65.
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    Cited by:

    1. Erel Segal-Halevi & Warut Suksompong, 2023. "Cutting a Cake Fairly for Groups Revisited," Papers 2301.09061, arXiv.org.
    2. Masoud Seddighin & Hamed Saleh & Mohammad Ghodsi, 2021. "Maximin share guarantee for goods with positive externalities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(2), pages 291-324, February.
    3. Bade, Sophie & Segal-Halevi, Erel, 2023. "Fairness for multi-self agents," Games and Economic Behavior, Elsevier, vol. 141(C), pages 321-336.
    4. Pasin Manurangsi & Warut Suksompong, 2020. "Closing Gaps in Asymptotic Fair Division," Papers 2004.05563, arXiv.org.
    5. Uriel Feige & Yehonatan Tahan, 2022. "On allocations that give intersecting groups their fair share," Papers 2204.06820, arXiv.org.
    6. Sophie Bade & Erel Segal-Halevi, 2018. "Fairness for Multi-Self Agents," Papers 1811.06684, arXiv.org, revised Apr 2022.
    7. Bentert, Matthias & Boehmer, Niclas & Heeger, Klaus & Koana, Tomohiro, 2023. "Stable matching with multilayer approval preferences: Approvals can be harder than strict preferences," Games and Economic Behavior, Elsevier, vol. 142(C), pages 508-526.

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