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Rental harmony with roommates

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  • Azrieli, Yaron
  • Shmaya, Eran

Abstract

We prove existence of envy-free allocations in markets with heterogenous indivisible goods and money, when a given quantity is supplied from each of the goods and agents have unit demands. We depart from most of the previous literature by allowing agents' preferences over the goods to depend on the entire vector of prices. We then show how our theorem may be applied in two related problems: Existence of envy-free allocations in a version of the cake-cutting problem, and existence of equilibrium in an exchange economy with indivisible goods and money. Our proof uses Shapley's K-K-M-S theorem and Hall's marriage lemma.

Suggested Citation

  • Azrieli, Yaron & Shmaya, Eran, 2014. "Rental harmony with roommates," Journal of Economic Theory, Elsevier, vol. 153(C), pages 128-137.
    • Handle: RePEc:eee:jetheo:v:153:y:2014:i:c:p:128-137
    DOI: 10.1016/j.jet.2014.06.006
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    Cited by:

    1. Anna Bogomolnaia & Hervé Moulin & Fedor Sandomirskiy & Elena Yanovskaya, 2017. "Competitive Division of a Mixed Manna," Econometrica, Econometric Society, vol. 85(6), pages 1847-1871, November.
    2. Erel Segal-Halevi, 2019. "Generalized Rental Harmony," Papers 1912.13249, arXiv.org, revised Feb 2020.
    3. Francisco Sánchez Sánchez, 2022. "Envy-Free Solutions to the Problem of Room Assignment and Rent Division," Group Decision and Negotiation, Springer, vol. 31(3), pages 703-721, June.
    4. Segal-Halevi, Erel & Nitzan, Shmuel & Hassidim, Avinatan & Aumann, Yonatan, 2017. "Fair and square: Cake-cutting in two dimensions," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 1-28.
    5. Erel Segal-Halevi & Shmuel Nitzan & Avinatan Hassidim & Yonatan Aumann, 2020. "Envy-Free Division of Land," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 896-922, August.
    6. Erel Segal-Halevi & Warut Suksompong, 2020. "How to Cut a Cake Fairly: A Generalization to Groups," Papers 2001.03327, arXiv.org, revised Apr 2020.
    7. Velez, Rodrigo A., 2016. "Fairness and externalities," Theoretical Economics, Econometric Society, vol. 11(1), January.

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    More about this item

    Keywords

    Envy-free; Assignment problem; Rental harmony; Cake cutting;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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