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The core for housing markets with limited externalities

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  • Bettina Klaus
  • Claudia Meo

Abstract

We propose a variant of the housing market model a la Shapley and Scarf (1974) that incorporates a limited form of externality in consumption; that is, agents care both about their own consumption (demand preferences) and about the agent who receives their endowment (supply preferences).We consider different domains of preference relations by taking demand and supply aspects of preferences into account. First, for markets with three agents who have (additive) separable preferences such that all houses and agents are acceptable, the strong core is nonempty; a result that can be neither extended to the unacceptable case nor to markets with a larger number of agents. Second, for markets where all agents have demand lexicographic preferences (or all of them have supply lexicographic preferences), we show that the strong core is nonempty, independent of the number of agents and the acceptability of houses or agents, and possibly multi-valued.

Suggested Citation

  • Bettina Klaus & Claudia Meo, 2021. "The core for housing markets with limited externalities," Cahiers de Recherches Economiques du Département d'économie 21.03a, Université de Lausanne, Faculté des HEC, Département d’économie.
    • Handle: RePEc:lau:crdeep:21.03a
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    References listed on IDEAS

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    1. Patrick Harless & William Phan, 2020. "On endowments and indivisibility: partial ownership in the Shapley–Scarf model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(2), pages 411-435, September.
    2. Sasaki, Hiroo & Toda, Manabu, 1996. "Two-Sided Matching Problems with Externalities," Journal of Economic Theory, Elsevier, vol. 70(1), pages 93-108, July.
    3. Hong, Miho & Park, Jaeok, 2022. "Core and top trading cycles in a market with indivisible goods and externalities," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    4. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    5. Maria Gabriella Graziano & Claudia Meo & Nicholas C. Yannelis, 2020. "Shapley and Scarf housing markets with consumption externalities," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 22(5), pages 1481-1514, September.
    6. Ismail Saglam & Ayse Mumcu, 2007. "The core of a housing market with externalities," Economics Bulletin, AccessEcon, vol. 3(57), pages 1-5.
    7. Roth, Alvin E. & Postlewaite, Andrew, 1977. "Weak versus strong domination in a market with indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 131-137, August.
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    Cited by:

    1. Maria Gabriella Graziano & Vincenzo Platino, 2024. "A measure of social loss for production economies with externalities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(2), pages 443-474, September.
    2. Battal Doğan & M. Bumin Yenmez, 2023. "When does an additional stage improve welfare in centralized assignment?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(4), pages 1145-1173, November.
    3. Yan Long, 2024. "Achieving the maximum size for exchange problems with dichotomous preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(2), pages 649-669, September.
    4. Piazza, Adriana & Torres-Martínez, Juan Pablo, 2024. "Coalitional stability in matching problems with externalities and random preferences," Games and Economic Behavior, Elsevier, vol. 143(C), pages 321-339.
    5. Bettina Klaus, 2024. "Characterizing the top trading cycles rule for housing markets with lexicographic preferences," Papers 2410.16745, arXiv.org.
    6. Hong, Miho & Park, Jaeok, 2022. "Core and top trading cycles in a market with indivisible goods and externalities," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    7. Afacan, Mustafa Oğuz & Hu, Gaoji & Li, Jiangtao, 2024. "Housing markets since Shapley and Scarf," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    8. Hadi Hosseini & Aghaheybat Mammadov & Tomasz Wk{a}s, 2024. "Almost Envy-Freeness under Weakly Lexicographic Preferences," Papers 2404.19740, arXiv.org.

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    More about this item

    Keywords

    Externalities; housing markets; weak core; strong core;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • D64 - Microeconomics - - Welfare Economics - - - Altruism; Philanthropy; Intergenerational Transfers

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