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Stability in coalition formation games

Author

Listed:
  • Antonio Romero-Medina

    (Departamento de Economia, Universidad Carlos III, 28903 Getafe, Spain)

  • Katari´na Cechlárová

    (Department of Geometry and Algebra, P. J. Safárik University, Jesenná 5, 041 54 Kosice, Slovakia)

Abstract

In the context of coalition formation games a player evaluates a partition on the basis of the set she belongs to. For this evaluation to be possible, players are supposed to have preferences over sets to which they could belong. In this paper, we suggest two extensions of preferences over individuals to preferences over sets. For the first one, derived from the most preferred member of a set, it is shown that a strict core partition always exists if the original preferences are strict and a simple algorithm for the computation of one strict core partition is derived. This algorithm turns out to be strategy proof. The second extension, based on the least preferred member of a set, produces solutions very similar to those for the stable roommates problem.

Suggested Citation

  • Antonio Romero-Medina & Katari´na Cechlárová, 2001. "Stability in coalition formation games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 487-494.
    • Handle: RePEc:spr:jogath:v:29:y:2001:i:4:p:487-494
    Note: Received August 1998/Final version June 20, 2000
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    Cited by:

    1. Dinko Dimitrov & Shao Chin Sung, 2006. "A Taxonomy of Myopic Stability Concepts for Hedonic Games," Working Papers 2006.10, Fondazione Eni Enrico Mattei.
    2. Alcalde, Jose & Revilla, Pablo, 2004. "Researching with whom? Stability and manipulation," Journal of Mathematical Economics, Elsevier, vol. 40(8), pages 869-887, December.
    3. Watts, Alison, 2006. "Formation of Segregated and Integrated Groups," Coalition Theory Network Working Papers 12171, Fondazione Eni Enrico Mattei (FEEM).
    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. Steven Brams & Michael Jones & D. Kilgour, 2005. "Forming stable coalitions: The process matters," Public Choice, Springer, vol. 125(1), pages 67-94, July.
    6. 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.
    7. 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).
    8. Carmelo Rodriguez-Alvarez, 2004. "On the Impossibility of Strategy-Proof Coalition Formation Rules," Economics Bulletin, AccessEcon, vol. 4(10), pages 1-8.
    9. Carmelo Rodríguez-Álvarez, 2009. "Strategy-proof coalition formation," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(3), pages 431-452, November.
    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. 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.
    12. Masaki Aoyagi, 2020. "Connecting Heterogeneous Agents under Incomplete Information," ISER Discussion Paper 1089, Institute of Social and Economic Research, Osaka University.
    13. Alison Watts, 2006. "Formation of Segregated and Integrated Groups," Working Papers 2006.127, Fondazione Eni Enrico Mattei.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Suksompong, Warut, 2015. "Individual and group stability in neutral restrictions of hedonic games," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 1-5.
    19. 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.
    20. Papai, Szilvia, 2004. "Unique stability in simple coalition formation games," Games and Economic Behavior, Elsevier, vol. 48(2), pages 337-354, August.
    21. 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.

    More about this item

    Keywords

    Coalition formation games · core · stable roommates problem · digraphs · algorithms.;

    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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