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Dynamic Club Formation with Coordination

Author

Listed:
  • Tone Arnold

    (Department of Economics, University of Hohenheim)

  • Myrna Wooders

    (Department of Economics, Vanderbilt University)

Abstract
We present a dynamic model of club formation in a society of identical people. Coalitions consisting of members of the same club can form for one period and coalition members can jointly deviate. The dynamic process is described by a Markov chain defined by myopic optimization on the part of coalitions. We define a Nash club equilibrium (NCE) as a strategy profile that is immune to such coalitional deviations. For single--peaked preferences, we show that, if one exists, the process will converge to a NCE profile with probability one. NCE is unique up to a renaming of players and locations. Further, NCE corresponds to strong Nash equilibrium in the club formation game. Finally, we deal with the case where NCE fails to exist due to a nonbalancedness problem. When the population size is not an integer multiple of an optimal club size, there may be 'left over' players who prevent the process from `settling down'. To treat this case, we define the concept of k-remainder NCE, which requires that all but k players are playing a Nash club equilibrium, where k is defined by the minimal number of left over players. We show that the process converges to an ergodic NCE, that is, a set of states consisting only of k-remainder NCE.

Suggested Citation

  • Tone Arnold & Myrna Wooders, 2005. "Dynamic Club Formation with Coordination," Vanderbilt University Department of Economics Working Papers 0522, Vanderbilt University Department of Economics.
    • Handle: RePEc:van:wpaper:0522
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    References listed on IDEAS

    as
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    Citations

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    Cited by:

    1. Anna Bogomolnaia & Antonio Nicolò, 2005. "Stable Assignment of Public Facilities under Congestion," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 7(1), pages 65-91, February.
    2. Ben Zissimos, 2011. "Why are Trade Agreements Regional?," Review of International Economics, Wiley Blackwell, vol. 19(1), pages 32-45, February.
    3. T. K. Ahn & R. Mark Isaac & Timothy C. Salmon, 2008. "Endogenous Group Formation," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(2), pages 171-194, April.
    4. Frank H. Page, Jr. & Myrna H. Wooders, 2005. "Club Formation Games with Farsighted Agents," Vanderbilt University Department of Economics Working Papers 0529, Vanderbilt University Department of Economics.
    5. Page Jr., Frank H. & Wooders, Myrna, 2007. "Networks and clubs," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 406-425.
    6. Page Jr., Frank H. & Wooders, Myrna, 2009. "Strategic basins of attraction, the path dominance core, and network formation games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 462-487, May.
    7. Andrea Robbett, 2015. "Voting with hands and feet: the requirements for optimal group formation," Experimental Economics, Springer;Economic Science Association, vol. 18(3), pages 522-541, September.
    8. Fershtman, Chaim & Persitz, Dotan, 2018. "Social Clubs and Social Networks," CEPR Discussion Papers 12874, C.E.P.R. Discussion Papers.
    9. Katharine A. Anderson, "undated". "Group Formation with a Network Constraint," GSIA Working Papers 2012-E49, Carnegie Mellon University, Tepper School of Business.

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    More about this item

    Keywords

    Club formation; cooperation; best-reply dynamics; Nash club equilibrium; ergodic Nash club equilibrium;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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