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In a housing market of Shapley and Scarf, each agent is endowed with oneindivisible object and has preferences over all objects. An allocation of theobjects 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 strongcore allocation (or competitive allocation) respects improvement: if an agent'sobject becomes more attractive for some other agents, then the agent'sallotment in the unique strong core allocation weakly improves. We obtain ageneral result in case of ties in the preferences and provide new integerprogramming formulations for computing (strong) core and competitiveallocations. Finally, we conduct computer simulations to compare thegame-theoretical solutions with maximum size and maximum weight exchanges formarkets that resemble the pools of kidney exchange programmes.

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