The Core of Housing Markets from an Agent’s Perspective: Is It Worth Sprucing up Your Home?

Ildikó Schlotter (), Péter Biró () and Tamás Fleiner ()
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Ildikó Schlotter: HUN-REN Centre for Economic and Regional Studies, Budapest 1097, Hungary; and Budapest University of Technology and Economics, Budapest 1111, Hungary
Péter Biró: HUN-REN Centre for Economic and Regional Studies, Budapest 1097, Hungary; and Corvinus University of Budapest, Budapest 1093, Hungary
Tamás Fleiner: HUN-REN Centre for Economic and Regional Studies, Budapest 1097, Hungary; and Budapest University of Technology and Economics, Budapest 1111, Hungary

Mathematics of Operations Research, 2025, vol. 50, issue 3, 2199-2225

Abstract: We study housing markets as introduced by Shapley and Scarf. 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 NP -hard to find an allocation in the core of H in which (i) a receives a certain house, (ii) a does not receive a certain house, or (iii) a receives a house other than a ’s own. We prove that the core of housing markets respects improvement in the following sense: given an allocation in the core of H in which 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 S table R oommates setting by proving that stable matchings in a one-sided market also respect improvement.

Keywords: Primary: 91A68; secondary: 68Q17; 91B52; 91B54; 91B68; housing market; core; computational complexity; respecting improvement; stable roommates (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:50:y:2025:i:3:p:2199-2225

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