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

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Main Authors: Schlotter, Ildikó, Biró, Péter, Fleiner, Tamás
Format: Preprint
Published: 2021
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author Schlotter, Ildikó
Biró, Péter
Fleiner, Tamás
author_facet Schlotter, Ildikó
Biró, Péter
Fleiner, Tamás
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2110_06875
institution arXiv
publishDate 2021
record_format arxiv
spellingShingle The core of housing markets from an agent's perspective: Is it worth sprucing up your home?
Schlotter, Ildikó
Biró, Péter
Fleiner, Tamás
Computer Science and Game Theory
Data Structures and Algorithms
91A68, 68Q17, 91B52, 91B54, 91B68
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.
title The core of housing markets from an agent's perspective: Is it worth sprucing up your home?
topic Computer Science and Game Theory
Data Structures and Algorithms
91A68, 68Q17, 91B52, 91B54, 91B68
url https://arxiv.org/abs/2110.06875