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Shapley-Scarf Housing Markets: Respecting Improvement, Integer Programming, and Kidney Exchange

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  • P'eter Bir'o
  • Flip Klijn
  • Xenia Klimentova
  • Ana Viana

Abstract

In a housing market of Shapley and Scarf, each agent is endowed with one indivisible object and has preferences over all objects. An allocation of the objects is in the (strong) core if there exists no (weakly) blocking coalition. In this paper we show that in the case of strict preferences the unique strong core allocation (or competitive allocation) respects improvement: if an agent's object becomes more attractive for some other agents, then the agent's allotment in the unique strong core allocation weakly improves. We obtain a general result in case of ties in the preferences and provide new integer programming formulations for computing (strong) core and competitive allocations. Finally, we conduct computer simulations to compare the game-theoretical solutions with maximum size and maximum weight exchanges for markets that resemble the pools of kidney exchange programmes.

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  • P'eter Bir'o & Flip Klijn & Xenia Klimentova & Ana Viana, 2021. "Shapley-Scarf Housing Markets: Respecting Improvement, Integer Programming, and Kidney Exchange," Papers 2102.00167, arXiv.org.
    • Handle: RePEc:arx:papers:2102.00167
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    1. Jorgen Kratz, "undated". "Conflicting Objectives in Kidney Exchange," Discussion Papers 23/04, Department of Economics, University of York.

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    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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