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Dynamic Club Formation with Coordination

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  • Arnold, Tone
  • Wooders, Myrna

Abstract

We present a dynamic model of jurisdiction formation in a society of identical people. The process is described by a Markov chain that is de¯ned by myopic optimization on the part of the players. We show that the process will converge to a Nash equilibrium club structure. Next, we allow for coordination between members of the same club, i. e. club members can form coalitions for one period and deviate jointly. We de¯ne a Nash club equilibrium (NCE) as a strategy con¯guration that is immune to such coalitional deviations. We show that, if one exists, this modi¯ed process will converge to a NCE con¯guration with probability one. Finally, we deal with the case where a NCE fails to exist due to indivisibility problems. When the population size is not an integer multiple of the optimal club size, there will be left over players who prevent the process from settling down. We de¯ne the concept of an approximate Nash club equilibrium (ANCE), which means that all but k players are playing a Nash club equilibrium, where k is de¯ned by the minimal number of left over players. We show that the modified process converges to an ergodic set of states each of which is ANCE.

Suggested Citation

  • Arnold, Tone & Wooders, Myrna, 2002. "Dynamic Club Formation with Coordination," Economic Research Papers 269414, University of Warwick - Department of Economics.
    • Handle: RePEc:ags:uwarer:269414
    DOI: 10.22004/ag.econ.269414
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Katharine A. Anderson, "undated". "Group Formation with a Network Constraint," GSIA Working Papers 2012-E49, Carnegie Mellon University, Tepper School of Business.
    5. Ben Zissimos, 2011. "Why are Trade Agreements Regional?," Review of International Economics, Wiley Blackwell, vol. 19(1), pages 32-45, February.
    6. Page Jr., Frank H. & Wooders, Myrna, 2007. "Networks and clubs," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 406-425.
    7. 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.
    8. Fershtman, Chaim & Persitz, Dotan, 2018. "Social Clubs and Social Networks," CEPR Discussion Papers 12874, C.E.P.R. Discussion Papers.
    9. 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.

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    More about this item

    Keywords

    Institutional and Behavioral Economics; Public Economics;

    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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