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A polynomial algorithm for maxmin and minmax envy-free rent division on a soft budget

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  • Rodrigo A. Velez

Abstract

The current practice of envy-free rent division, lead by the fair allocation website Spliddit, is based on quasi-linear preferences. These preferences rule out agents' well documented financial constraints. To resolve this issue we consider piece-wise linear budget constrained preferences. These preferences admit differences in agents' marginal disutility of paying rent below and above a given reference, i.e., a soft budget. We construct a polynomial algorithm to calculate a maxmin utility envy-free allocation, and other related solutions, in this domain.

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  • Rodrigo A. Velez, 2020. "A polynomial algorithm for maxmin and minmax envy-free rent division on a soft budget," Papers 2002.02966, arXiv.org.
    • Handle: RePEc:arx:papers:2002.02966
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    References listed on IDEAS

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    1. Rodrigo A. Velez, 2017. "Equitable rent division," Working Papers 20170818-001, Texas A&M University, Department of Economics.
    2. Alkan, Ahmet, 1989. "Existence and computation of matching equilibria," European Journal of Political Economy, Elsevier, vol. 5(2-3), pages 285-296.
    3. Gabrielle Demange & Ahmet Alkan & David Gale, 1991. "Fair Allocation of Indivisible Goods and Money and Criteria of Justice," Post-Print halshs-00670945, HAL.
    4. Alkan, Ahmet & Demange, Gabrielle & Gale, David, 1991. "Fair Allocation of Indivisible Goods and Criteria of Justice," Econometrica, Econometric Society, vol. 59(4), pages 1023-1039, July.
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