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

P\'eter Bir\'o, Flip Klijn, Xenia Klimentova and Ana Viana

Papers from arXiv.org

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.

Date: 2021-01
New Economics Papers: this item is included in nep-des
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Citations: View citations in EconPapers (2)

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Working Paper: Shapley-Scarf Housing Markets: Respecting Improvement, Integer Programming, and Kidney Exchange (2021)
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