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

Author

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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)

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.

Suggested Citation

  • Ildikó Schlotter & Péter Biró & Tamás Fleiner, 2025. "The Core of Housing Markets from an Agent’s Perspective: Is It Worth Sprucing up Your Home?," Mathematics of Operations Research, INFORMS, vol. 50(3), pages 2199-2225, August.
    • Handle: RePEc:inm:ormoor:v:50:y:2025:i:3:p:2199-2225
    DOI: 10.1287/moor.2023.0092
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