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arXiv · 2110.06875

The core of housing markets from an agent's perspective: Is it worth sprucing up your home?

Ildikó Schlotter·Péter Biró·Tamás Fleiner
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Abstract

We study housing markets as introduced by Shapley and Scarf (1974). We investigate the computational complexity of various questions regarding the situation of an agent $a$ in a housing market $H$: we show that it is $\mathsf{NP}$-hard to find an allocation in the core of $H$ where (i) $a$ receives a certain house, (ii) $a$ does not receive a certain house, or (iii) $a$ receives a house other than her own. We prove that the core of housing markets respects improvement in the following sense: given an allocation in the core 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 in its core in which $a$ receives either $h$, or a house that $a$ prefers to $h$; moreover, such an allocation can be found efficiently. We further show an analogous result in the Stable Roommates setting by proving that stable matchings in a one-sided market also respect improvement.

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Ildikó Schlotter, Péter Biró, Tamás Fleiner. 2021-10-13. The core of housing markets from an agent's perspective: Is it worth sprucing up your home?. https://arxiv.org/abs/2110.06875

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