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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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    1. Eric S. Maskin, 1987. "On the Fair Allocation of Indivisible Goods," Palgrave Macmillan Books, in: George R. Feiwel (ed.), Arrow and the Foundations of the Theory of Economic Policy, chapter 11, pages 341-349, Palgrave Macmillan.
    2. Shapley, Lloyd & Vohra, Rajiv, 1991. "On Kakutani's Fixed Point Theorem, the K-K-M-S Theorem and the Core of a Balanced Game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 108-116, January.
    3. Atila Abdulkadiroğlu & Tayfun Sönmez & M. Utku Ünver, 2004. "Room assignment-rent division: A market approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(3), pages 515-538, June.
    4. Demange, Gabrielle & Gale, David & Sotomayor, Marilda, 1986. "Multi-Item Auctions," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 863-872, August.
    5. Ichiishi, Tatsuro & Idzik, Adam, 1999. "Equitable allocation of divisible goods," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 389-400, December.
    6. Zhou, Lin, 1994. "A Theorem on Open Coverings of a Simplex and Scarf's Core Existence Theorem through Brouwer's Fixed Point Theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(3), pages 473-477, May.
    7. Tadenuma, Koichi & Thomson, William, 1991. "No-Envy and Consistency in Economies with Indivisible Goods," Econometrica, Econometric Society, vol. 59(6), pages 1755-1767, November.
    8. Svensson, Lars-Gunnar, 1983. "Large Indivisibles: An Analysis with Respect to Price Equilibrium and Fairness," Econometrica, Econometric Society, vol. 51(4), pages 939-954, July.
    9. P. Jean-Jacques Herings, 1997. "An extremely simple proof of the K-K-M-S Theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(2), pages 361-367.
    10. 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.
    11. Varian, Hal R., 1974. "Equity, envy, and efficiency," Journal of Economic Theory, Elsevier, vol. 9(1), pages 63-91, September.
    12. Velez, Rodrigo A., 2011. "Are incentives against economic justice?," Journal of Economic Theory, Elsevier, vol. 146(1), pages 326-345, January.
    13. Ichiishi, Tatsuro & Idzik, Adam, 1999. "Market allocation of indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 457-466, December.
    14. Velez, Rodrigo A., 2016. "Fairness and externalities," Theoretical Economics, Econometric Society, vol. 11(1), January.
    15. Komiya, Hidetoshi, 1994. "A Simple Proof of K-K-M-S Theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(3), pages 463-466, May.
    16. Zhou Lin, 1994. "A New Bargaining Set of an N-Person Game and Endogenous Coalition Formation," Games and Economic Behavior, Elsevier, vol. 6(3), pages 512-526, May.
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    Cited by:

    1. 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.
    2. 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.
    3. Erel Segal-Halevi & Warut Suksompong, 2020. "How to Cut a Cake Fairly: A Generalization to Groups," Papers 2001.03327, arXiv.org, revised Apr 2020.
    4. 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.
    5. Erel Segal-Halevi, 2019. "Generalized Rental Harmony," Papers 1912.13249, arXiv.org, revised Feb 2020.
    6. 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.
    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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