We study housing markets as introduced by Shapley and Scarf (1974) We prove that the core of housingmarkets respects improvement in the following sense: given an allocation in thecore of $H$ where agent $a$ receives a house $h$ if the value of the house owned by $a$. increases, then the resulting housing market admits an allocation where $a receives a house that she prefers to $h$. We further show an analogousresult in the Stable Roommates setting by proving that stable matchings in aone-sided market also respect improvement . We further prove that stable matching matches in a one-sided setting also respectimprovements in a single-sided housing market . We conclude that stable

Author(s) : Ildikó Schlotter, Péter Biró, Tamás Fleiner

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Keywords : stable - housing - market - sided - house -

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