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

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Web and Internet Economics (WINE 2021)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 13112))

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Abstract

We study housing markets as introduced by Shapley and Scarf [39]. 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 where a receives either h, or a house that she 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.

Supported by the Hungarian Academy of Sciences (Momentum Programme LP2021-2) and the Hungarian Scientific Research Fund (NFKIH grants K128611, K124171).

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Notes

  1. 1.

    Throughout the paper we will use the term partial ordering in the sense of an irreflexive (or strict) partial ordering.

  2. 2.

    In fact, these are the two factors for which acceptability thresholds can be set by the patients in the UK program [8].

  3. 3.

    Proofs marked by an asterisk can be found in the full version of our paper [38].

  4. 4.

    The first claim of the lemma is only implicit in the paper by Tan and Hsueh [41], we prove it for the sake of completeness in the full version of our paper [38].

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Authors and Affiliations

  1. Centre for Economic and Regional Studies, Budapest, Hungary

    Ildikó Schlotter, Péter Biró & Tamás Fleiner

  2. Budapest University of Technology and Economics, Budapest, Hungary

    Ildikó Schlotter & Tamás Fleiner

  3. Corvinus University of Budapest, Budapest, Hungary

    Péter Biró

Authors
  1. Ildikó Schlotter
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  2. Péter Biró
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  3. Tamás Fleiner
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Correspondence to Ildikó Schlotter .

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Editors and Affiliations

  1. Tel Aviv University, Tel Aviv, Israel

    Michal Feldman

  2. Shanghai University of Finance and Economics, Shanghai, China

    Hu Fu

  3. Technion – Israel Institute of Technology, Haifa, Israel

    Inbal Talgam-Cohen

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Schlotter, I., Biró, P., Fleiner, T. (2022). The Core of Housing Markets from an Agent’s Perspective: Is It Worth Sprucing Up Your Home?. In: Feldman, M., Fu, H., Talgam-Cohen, I. (eds) Web and Internet Economics. WINE 2021. Lecture Notes in Computer Science(), vol 13112. Springer, Cham. https://doi.org/10.1007/978-3-030-94676-0_14

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  • DOI: https://doi.org/10.1007/978-3-030-94676-0_14

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