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Consistency and its Converse for Roommate Markets

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  • Bettina Klaus

Abstract

For classical marriage markets with equal numbers of men and women and where all men find all women acceptable and all women find all men acceptable, Sasaki and Toda (1992) characterized the core by same-side anonymity for marriage markets, Pareto optimality, consistency, and converse consistency. Nizamogullari and Ozkal-Sanver (2014) generalized this result to the domain of classical marriage markets by adding individual rationality and replacing same-side anonymity for marriage markets with a stronger property called gender fairness. We generalize both results by characterizing the core on the domain of solvable roommate markets without so-called ``3-rings'' (and on the domain of marriage markets) by individual rationality, anonymity, Pareto optimality, consistency, and converse consistency. We also prove that extending this characterization to the domain of solvable roommate markets is not possible.

Suggested Citation

  • Bettina Klaus, 2017. "Consistency and its Converse for Roommate Markets," Cahiers de Recherches Economiques du Département d'économie 17.03, Université de Lausanne, Faculté des HEC, Département d’économie.
    • Handle: RePEc:lau:crdeep:17.03
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    1. Özkal-Sanver, Ipek, 2010. "Impossibilities for roommate problems," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 360-363, May.
    2. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November.
    3. Inada, Ken-Ichi, 1969. "The Simple Majority Decision Rule," Econometrica, Econometric Society, vol. 37(3), pages 490-506, July.
    4. Sen, Amartya & Pattanaik, Prasanta K., 1969. "Necessary and sufficient conditions for rational choice under majority decision," Journal of Economic Theory, Elsevier, vol. 1(2), pages 178-202, August.
    5. Burak Can & Bettina Klaus, 2013. "Consistency and population sensitivity properties in marriage and roommate markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 835-862, October.
    6. Klaus, Bettina, 2011. "Competition and resource sensitivity in marriage and roommate markets," Games and Economic Behavior, Elsevier, vol. 72(1), pages 172-186, May.
    7. Becker, Gary S, 1973. "A Theory of Marriage: Part I," Journal of Political Economy, University of Chicago Press, vol. 81(4), pages 813-846, July-Aug..
    8. 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.
    9. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    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.
    11. Ozkal-Sanver, Ipek, 2004. "A note on gender fairness in matching problems," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 211-217, March.
    12. 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.
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    Cited by:

    1. Can, Burak & Pourpouneh, Mohsen & Storcken, Ton, 2017. "Cost of transformation: a measure on matchings," Research Memorandum 015, Maastricht University, Graduate School of Business and Economics (GSBE).
    2. Stéphane Gonzalez & Aymeric Lardon, 2018. "Axiomatic foundations of a unifying concept of the core of games in effectiveness form," Post-Print halshs-01902122, HAL.
    3. Stéphane Gonzalez & Aymeric Lardon, 2018. "Axiomatic Foundations of a Unifying Core," Working Papers 1817, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    4. Gonzalez, Stéphane & Lardon, Aymeric, 2021. "Axiomatic foundations of the core for games in effectiveness form," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 28-38.
    5. 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.
    6. Karpov, Alexander, 2019. "A necessary and sufficient condition for uniqueness consistency in the stable marriage matching problem," Economics Letters, Elsevier, vol. 178(C), pages 63-65.
    7. Can, Burak & Pourpouneh, Mohsen & Storcken, Ton, 2023. "Distance on matchings: an axiomatic approach," Theoretical Economics, Econometric Society, vol. 18(2), May.
    8. 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

    Converse Consistency; 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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