IDEAS home Printed from https://ideas.repec.org/p/lau/crdeep/17.03.html
   My bibliography  Save this paper

Consistency and its Converse for Roommate Markets

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hec.unil.ch/attachments/deep/series/2016/17.03.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. 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.
    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. Ozkal-Sanver, Ipek, 2004. "A note on gender fairness in matching problems," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 211-217, March.
    8. 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.
    9. 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.
    10. 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..
    11. 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.
    12. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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," GREDEG Working Papers 2018-15, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    3. repec:hal:journl:hal-04797842 is not listed on IDEAS
    4. 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.
    5. 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.
    6. Stéphane Gonzalez & Aymeric Lardon, 2018. "Axiomatic Foundations of a Unifying Core," Working Papers halshs-01930836, HAL.
    7. Can, Burak & Pourpouneh, Mohsen & Storcken, Ton, 2023. "Distance on matchings: an axiomatic approach," Theoretical Economics, Econometric Society, vol. 18(2), May.
    8. 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.
    9. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kasajima, Yoichi & Toda, Manabu, 2024. "Singles monotonicity and stability in one-to-one matching problems," Games and Economic Behavior, Elsevier, vol. 143(C), pages 269-286.
    2. 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.
    3. Duygu Nizamogullari & İpek Özkal-Sanver, 2015. "Consistent enlargements of the core in roommate problems," Theory and Decision, Springer, vol. 79(2), pages 217-225, September.
    4. 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.
    5. Peter Biro & Elena Iñarra & Elena Molis, 2014. "A new solution for the roommate problem. The Q-stable matchings," ThE Papers 14/04, Department of Economic Theory and Economic History of the University of Granada..
    6. 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.
    7. 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.
    8. 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.
    9. Özkal-Sanver, Ipek, 2010. "Impossibilities for roommate problems," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 360-363, May.
    10. 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.
    11. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November.
    12. İpek Özkal-Sanver, 2013. "Minimal conversely consistent extension of the men-optimal solution," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 89-99, January.
    13. 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.
    14. 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).
    15. Steven F. Koch, 2005. "Love and Addiction: The Importance of Commitment," Working Papers 200516, University of Pretoria, Department of Economics.
    16. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
    17. Bettina Klaus & David F. Manlove & Francesca Rossi, 2014. "Matching under Preferences," Cahiers de Recherches Economiques du Département d'économie 14.07, Université de Lausanne, Faculté des HEC, Département d’économie.
    18. Pierre-André Chiappori & Alfred Galichon & Bernard Salanié, 2012. "The Roommate Problem is More Stable than You Think," Working Papers hal-03588302, HAL.
    19. Justin Leroux, 2006. "A discussion of the consistency axiom in cost-allocation problems," Cahiers de recherche 06-13, HEC Montréal, Institut d'économie appliquée.
    20. Can, Burak & Pourpouneh, Mohsen & Storcken, Ton, 2023. "Distance on matchings: an axiomatic approach," Theoretical Economics, Econometric Society, vol. 18(2), May.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:lau:crdeep:17.03. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Christina Seld (email available below). General contact details of provider: https://edirc.repec.org/data/deelsch.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.