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Dynamic Club Formation with Coordination

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  • 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.

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File URL: http://www.accessecon.com/pubs/VUECON/vu05-w22.pdf
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Bibliographic Info

Paper provided by Vanderbilt University Department of Economics in its series Vanderbilt University Department of Economics Working Papers with number 0522.

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Date of creation: Sep 2005
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Handle: RePEc:van:wpaper:0522

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Web page: http://www.vanderbilt.edu/econ/wparchive/index.html

Related research

Keywords: Club formation; cooperation; best-reply dynamics; Nash club equilibrium; ergodic Nash club equilibrium;

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References

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  1. Barham, V. & Wooders, M.H., 1994. "First and Second Welfare Theorems for Economies with Collective Goods," Working Papers 9415e, University of Ottawa, Department of Economics.
  2. Wooders, Myrna, 1980. "The Tiebout Hypothesis: Near Optimality in Local Public Good Economies," Econometrica, Econometric Society, vol. 48(6), pages 1467-85, September.
  3. Alexander Kovalenkov & Myrna H. Wooders, 1998. "Approximate cores of games and economies with clubs," Working Papers mwooders-00-01, University of Toronto, Department of Economics.
  4. Milchtaich, Igal & Winter, Eyal, 2002. "Stability and Segregation in Group Formation," Games and Economic Behavior, Elsevier, vol. 38(2), pages 318-346, February.
  5. Konishi, Hideo & Weber, Shlomo & Le Breton, Michel, 1997. "Free mobility equilibrium in a local public goods economy with congestion," Research in Economics, Elsevier, vol. 51(1), pages 19-30, April.
  6. Martin Shubik, 1969. "The 'Bridge Game' Economy," Cowles Foundation Discussion Papers 267, Cowles Foundation for Research in Economics, Yale University.
  7. Arnold, Tone & Schwalbe, Ulrich, 2002. "Dynamic coalition formation and the core," Journal of Economic Behavior & Organization, Elsevier, vol. 49(3), pages 363-380, November.
  8. Conley, John P. & Wooders, Myrna H., 1997. "Equivalence of the Core and Competitive Equilibrium in a Tiebout Economy with Crowding Types," Journal of Urban Economics, Elsevier, vol. 41(3), pages 421-440, May.
  9. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-71, September.
  10. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1998. "Equilibrium in a Finite Local Public Goods Economy," Journal of Economic Theory, Elsevier, vol. 79(2), pages 224-244, April.
  11. Ray, D. & Vohra, R., 1993. "Equilibrium Binding Agreements," Papers 21, Boston University - Department of Economics.
  12. Holzman, Ron & Law-Yone, Nissan, 1997. "Strong Equilibrium in Congestion Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 85-101, October.
  13. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
  14. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1997. "Equilibria in a Model with Partial Rivalry," Journal of Economic Theory, Elsevier, vol. 72(1), pages 225-237, January.
  15. Hollard, Guillaume, 2000. "On the existence of a pure strategy Nash equilibrium in group formation games," Economics Letters, Elsevier, vol. 66(3), pages 283-287, March.
  16. Slikker, Marco & Dutta, Bhaskar & van den Nouweland, Anne & Tijs, Stef, 2000. "Potential maximizers and network formation," Mathematical Social Sciences, Elsevier, vol. 39(1), pages 55-70, January.
  17. Conley, John P. & Wooders, Myrna H., 2001. "Tiebout Economies with Differential Genetic Types and Endogenously Chosen Crowding Characteristics," Journal of Economic Theory, Elsevier, vol. 98(2), pages 261-294, June.
  18. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1997. "Pure Strategy Nash Equilibrium in a Group Formation Game with Positive Externalities," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 161-182, October.
  19. Dieckmann, Tone, 1999. "The evolution of conventions with mobile players," Journal of Economic Behavior & Organization, Elsevier, vol. 38(1), pages 93-111, January.
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Cited by:
  1. Ben Zissimos, 2007. "Why are Trade Agreements Regional?," Working Papers 2007.67, Fondazione Eni Enrico Mattei.
  2. Frank H. Page, Jr. & Myrna H. Wooders, 2006. "Strategic Basins of Attraction, the Path Dominance Core, and Network Formation Games," Vanderbilt University Department of Economics Working Papers 0614, Vanderbilt University Department of Economics.
  3. 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.
  4. Page Jr., Frank H. & Wooders, Myrna, 2007. "Networks and clubs," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 406-425.

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