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Stability in one-sided matching markets

Author

Listed:
  • Romero-Medina, Antonio
  • Cechlárová, Katarína

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

  • Romero-Medina, Antonio & Cechlárová, Katarína, 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. Steven Brams & Michael Jones & D. Kilgour, 2005. "Forming stable coalitions: The process matters," Public Choice, Springer, vol. 125(1), pages 67-94, July.
    2. Dinko Dimitrov & Shao Chin Sung, 2006. "A Taxonomy of Myopic Stability Concepts for Hedonic Games," Working Papers 2006.10, Fondazione Eni Enrico Mattei.
    3. 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.
    4. 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).
    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. Carmelo Rodriguez-Alvarez, 2004. "On the Impossibility of Strategy-Proof Coalition Formation Rules," Economics Bulletin, AccessEcon, vol. 4(10), pages 1-8.
    7. Carmelo Rodríguez-Álvarez, 2009. "Strategy-proof coalition formation," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(3), pages 431-452, November.
    8. 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.
    9. Papai, Szilvia, 2004. "Unique stability in simple coalition formation games," Games and Economic Behavior, Elsevier, vol. 48(2), pages 337-354, August.
    10. Shao Sung & Dinko Dimitrov, 2007. "On Myopic Stability Concepts for Hedonic Games," Theory and Decision, Springer, vol. 62(1), pages 31-45, February.
    11. repec:wsi:ijitdm:v:03:y:2004:i:04:n:s0219622004001276 is not listed on IDEAS
    12. Alison Watts, 2006. "Formation of Segregated and Integrated Groups," Working Papers 2006.127, Fondazione Eni Enrico Mattei.
    13. 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.

    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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