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Preference revelation games and strict cores of multiple-type housing market problems

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  • Di Feng
  • Bettina Klaus

Abstract

We consider multiple-type housing market problems as introduced by Moulin (1995) and study the relationship between strict strong Nash equilibria and the strict core (two solution concepts that are defined in terms of the absence of weak blocking coalitions). We prove that for lexicographically separable preferences, the set of all strict strong Nash equilibrium outcomes of each preference revelation game that is induced by a strictly core-stable mechanism is a subset of the strict core, but not vice versa, i.e., there are strict core allocations that cannot be implemented in strict strong Nash equilibrium (Theorem 1). This result is extended to a more general set of preference domains that satisfy strict core non-emptiness and a minimal preference domain richness assumption (Theorem 2).

Suggested Citation

  • Di Feng & Bettina Klaus, 2021. "Preference revelation games and strict cores of multiple-type housing market problems," Cahiers de Recherches Economiques du Département d'économie 21.10, Université de Lausanne, Faculté des HEC, Département d’économie.
    • Handle: RePEc:lau:crdeep:21.10
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    2. Morrill, Thayer & Roth, Alvin E., 2024. "Top trading cycles," Journal of Mathematical Economics, Elsevier, vol. 112(C).
    3. Di Feng & Bettina Klaus & Flip Klijn, 2022. "A Characterization of the Coordinate-Wise Top-Trading-Cycles Mechanism for Multiple-Type Housing Markets," Cahiers de Recherches Economiques du Département d'économie 22.06, Université de Lausanne, Faculté des HEC, Département d’économie.
    4. Di Feng, 2023. "Endowments-swapping-proofness and Efficiency in Multiple-Type Housing Markets," Discussion Paper Series DP2023-14, Research Institute for Economics & Business Administration, Kobe University.
    5. Feng, Di & Klaus, Bettina & Klijn, Flip, 2024. "Characterizing the typewise top-trading-cycles mechanism for multiple-type housing markets," Games and Economic Behavior, Elsevier, vol. 146(C), pages 234-254.
    6. Di Feng, 2023. "Efficiency in Multiple-Type Housing Markets," Papers 2308.14989, arXiv.org, revised Feb 2025.
    7. Echenique, Federico & Goel, Sumit & Lee, SangMok, 2024. "Stable allocations in discrete exchange economies," Journal of Economic Theory, Elsevier, vol. 222(C).
    8. Feng, Di, 2025. "Efficiency in multiple-type housing markets," Journal of Mathematical Economics, Elsevier, vol. 119(C).

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    Keywords

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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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