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Stability in one-sided matching markets

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  • Cechlárová, Katarína
  • Romero-Medina, Antonio

Abstract

The stable roommates problem may be unsolvable for sorne instances, therefore we study a relaxation, when it is allowed to form groups of any size (the stable partition problem). Two extensions of preferences over individuals to preferences over sets are suggested. For the first one, derived from the most prefered member of a set, it is shown that a stable partition always existis if the original preferences are strict and a simple algorithm for its computation is derived. This algorithm turns out to be strategy proof. The second extension, based on the least prefered member of a set, produces solutions very similar to those for the stable roornmates problem.

Suggested Citation

  • Cechlárová, Katarína & Romero-Medina, Antonio, 1998. "Stability in one-sided matching markets," UC3M Working papers. Economics 4158, Universidad Carlos III de Madrid. Departamento de Economía.
    • Handle: RePEc:cte:werepe:4158
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    Cited by:

    1. Andreas Darmann, 2019. "Manipulability in a group activity selection problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(3), pages 527-557, March.
    2. Dinko Dimitrov & Peter Borm & Ruud Hendrickx & Shao Sung, 2006. "Simple Priorities and Core Stability in Hedonic Games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 421-433, April.
    3. 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.
    4. Abdou, Joseph M. & Keiding, Hans, 2019. "A qualitative theory of conflict resolution and political compromise," Mathematical Social Sciences, Elsevier, vol. 98(C), pages 15-25.
    5. Alcalde, Jose & Revilla, Pablo, 2004. "Researching with whom? Stability and manipulation," Journal of Mathematical Economics, Elsevier, vol. 40(8), pages 869-887, December.
    6. Alison Watts, 2007. "Formation of segregated and integrated groups," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(4), pages 505-519, April.
    7. Papai, Szilvia, 2004. "Unique stability in simple coalition formation games," Games and Economic Behavior, Elsevier, vol. 48(2), pages 337-354, August.
    8. Steven Brams & Michael Jones & D. Kilgour, 2005. "Forming stable coalitions: The process matters," Public Choice, Springer, vol. 125(1), pages 67-94, July.
    9. Dinko Dimitrov & Shao Chin Sung, 2006. "A Taxonomy of Myopic Stability Concepts for Hedonic Games," Working Papers 2006.10, Fondazione Eni Enrico Mattei.
    10. José Alcalde & Pablo Revilla, 2001. "Tops Responsiveness, Strategy-Proofness And Coalition Formation Problems," Working Papers. Serie AD 2001-11, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    11. Carmelo Rodriguez-Alvarez, 2004. "On the Impossibility of Strategy-Proof Coalition Formation Rules," Economics Bulletin, AccessEcon, vol. 4(10), pages 1-8.
    12. Carmelo Rodríguez-Álvarez, 2009. "Strategy-proof coalition formation," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(3), pages 431-452, November.
    13. Shao Sung & Dinko Dimitrov, 2007. "On Myopic Stability Concepts for Hedonic Games," Theory and Decision, Springer, vol. 62(1), pages 31-45, February.
    14. Katarína Cechlárová & Jana Hajduková, 2004. "STABILITY OF PARTITIONS UNDER$\mathcal{WB}$-PREFERENCES AND$\mathcal{BW}$-PREFERENCES," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 605-618.
    15. Masaki Aoyagi, 2020. "Connecting Heterogeneous Agents under Incomplete Information," ISER Discussion Paper 1089, Institute of Social and Economic Research, Osaka University.
    16. Watts, Alison, 2006. "Formation of Segregated and Integrated Groups," Coalition Theory Network Working Papers 12171, Fondazione Eni Enrico Mattei (FEEM).
    17. Alison Watts, 2006. "Formation of Segregated and Integrated Groups," Working Papers 2006.127, Fondazione Eni Enrico Mattei.
    18. Koji Takamiya, 2013. "Coalitional unanimity versus strategy-proofness in coalition formation problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 115-130, February.
    19. Katarína Cechlárová & Vladimír Lacko, 2012. "The kidney exchange problem: How hard is it to find a donor?," Annals of Operations Research, Springer, vol. 193(1), pages 255-271, March.
    20. Suksompong, Warut, 2015. "Individual and group stability in neutral restrictions of hedonic games," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 1-5.
    21. Rothe, Jörg & Schadrack, Hilmar & Schend, Lena, 2018. "Borda-induced hedonic games with friends, enemies, and neutral players," Mathematical Social Sciences, Elsevier, vol. 96(C), pages 21-36.

    More about this item

    Keywords

    Matching markets;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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