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Consistency and Population Sensitivity Properties in Marriage and Roommate Markets

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  • Burak Can
  • Bettina Klaus

Abstract

We consider one-to-one matching markets in which agents can either be matched as pairs or remain single. In these so-called roommate markets agents are consumers and resources at the same time. Klaus (2010) introduced two new "population sensitivity" properties that capture the effect newcomers have on incumbent agents: competition sensitivity and resource sensitivity. On various roommate market domains (marriage markets, no odd rings roommate markets, solvable roommate markets), we characterize the core using either of the population sensitivity properties in addition to weak unanimity and consistency. On the domain of all roommate markets, we obtain two associated impossibility results.

Suggested Citation

  • Burak Can & Bettina Klaus, 2010. "Consistency and Population Sensitivity Properties in Marriage and Roommate Markets," Cahiers de Recherches Economiques du Département d'économie 10.08, Université de Lausanne, Faculté des HEC, Département d’économie.
    • Handle: RePEc:lau:crdeep:10.08
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    References listed on IDEAS

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    1. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November.
    2. Diamantoudi, Effrosyni & Miyagawa, Eiichi & Xue, Licun, 2004. "Random paths to stability in the roommate problem," Games and Economic Behavior, Elsevier, vol. 48(1), pages 18-28, July.
    3. Klaus, Bettina, 2011. "Competition and resource sensitivity in marriage and roommate markets," Games and Economic Behavior, Elsevier, vol. 72(1), pages 172-186, May.
    4. Manabu Toda, 2006. "Monotonicity and Consistency in Matching Markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 13-31, April.
    5. Bettina Klaus & Flip Klijn, 2010. "Smith and Rawls share a room: stability and medians," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(4), pages 647-667, October.
    6. Sasaki, Hiroo & Toda, Manabu, 1992. "Consistency and characterization of the core of two-sided matching problems," Journal of Economic Theory, Elsevier, vol. 56(1), pages 218-227, February.
    7. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-1480, November.
    8. Crawford, Vincent P., 1991. "Comparative statics in matching markets," Journal of Economic Theory, Elsevier, vol. 54(2), pages 389-400, August.
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    Citations

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    Cited by:

    1. Paula Jaramillo, 2017. "Minimal consistent enlargements of the immediate acceptance rule and the top trading cycles rule in school choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 177-195, January.
    2. Klaus, Bettina, 2017. "Consistency and its converse for roommate markets," Games and Economic Behavior, Elsevier, vol. 104(C), pages 43-58.
    3. Klaus, Bettina, 2011. "Competition and resource sensitivity in marriage and roommate markets," Games and Economic Behavior, Elsevier, vol. 72(1), pages 172-186, May.
    4. Péter Biró & Elena Inarra & Elena Molis, 2014. "A new solution for the roommate problem: The Q-stable matchings," CERS-IE WORKING PAPERS 1422, Institute of Economics, Centre for Economic and Regional Studies.
    5. Sheida Etemadidavan & Andrew J. Collins, 2021. "An Empirical Distribution of the Number of Subsets in the Core Partitions of Hedonic Games," SN Operations Research Forum, Springer, vol. 2(4), pages 1-20, December.
    6. Biró, Péter & Iñarra, Elena & Molis, Elena, 2016. "A new solution concept for the roommate problem: Q-stable matchings," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 74-82.
    7. Yoichi Kasajima & Manabu Toda, 2021. "Singles monotonicity and stability in one-to-one matching problems," Working Papers 2023-1, Waseda University, Faculty of Political Science and Economics.
    8. Mehmet Karakaya & Bettina Klaus, 2017. "Hedonic coalition formation games with variable populations: core characterizations and (im)possibilities," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 435-455, May.
    9. Duygu Nizamogullari & İpek Özkal-Sanver, 2022. "A note on roommate problems with a limited number of rooms," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 553-560, December.
    10. Nizamogullari, Duygu & Özkal-Sanver, İpek, 2014. "Characterization of the core in full domain marriage problems," Mathematical Social Sciences, Elsevier, vol. 69(C), pages 34-42.

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    More about this item

    Keywords

    consistency; competition and resource sensitivity; core; marriage and roommate markets;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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