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Dynamic Club Formation With Coordination

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  • Arnold, Tone

    (Department of Economics, University of Hohenheim)

  • Wooders, Myrna

    (Department of Economics, University of Warwick)

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 defined 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 define a Nash club equilibrium (NCE) as a strategy configuration that is immune to such coalitional deviations. We show that, if one exists, this modified process will converge to a NCE configuration 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 define 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 defined 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.

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Bibliographic Info

Paper provided by University of Warwick, Department of Economics in its series The Warwick Economics Research Paper Series (TWERPS) with number 640.

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Length: 21 pages
Date of creation: 2002
Date of revision:
Handle: RePEc:wrk:warwec:640

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Keywords: Club formation ; Cooperation ; Best-reply dynamics ; Learning ; Approximate Nash club Equilibrium ; Approximate core.;

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References

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  1. 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.
  2. Barham, V. & Wooders, M.H., 1994. "First and Second Welfare Theorems for Economies with Collective Goods," Working Papers, University of Ottawa, Department of Economics 9415e, University of Ottawa, Department of Economics.
  3. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, Econometric Society, vol. 61(5), pages 1047-71, September.
  4. Holzman, Ron & Law-Yone, Nissan, 1997. "Strong Equilibrium in Congestion Games," Games and Economic Behavior, Elsevier, Elsevier, vol. 21(1-2), pages 85-101, October.
  5. Konishi, Hideo & Weber, Shlomo & Le Breton, Michel, 1997. "Free mobility equilibrium in a local public goods economy with congestion," Research in Economics, Elsevier, Elsevier, vol. 51(1), pages 19-30, April.
  6. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1997. "Equilibria in a Model with Partial Rivalry," Journal of Economic Theory, Elsevier, Elsevier, vol. 72(1), pages 225-237, January.
  7. Slikker, M. & Dutta, B. & Tijs, S.H. & Nouweland, C.G.A.M. van den, 2000. "Potential maximizers and network formation," Open Access publications from Tilburg University urn:nbn:nl:ui:12-84647, Tilburg University.
  8. Arnold, Tone & Schwalbe, Ulrich, 2002. "Dynamic coalition formation and the core," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 49(3), pages 363-380, November.
  9. 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.
  10. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, Elsevier, vol. 38(2), pages 201-230, February.
  11. Milchtaich, Igal & Winter, Eyal, 2002. "Stability and Segregation in Group Formation," Games and Economic Behavior, Elsevier, Elsevier, vol. 38(2), pages 318-346, February.
  12. 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, Elsevier, vol. 21(1-2), pages 161-182, October.
  13. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1998. "Equilibrium in a Finite Local Public Goods Economy," Journal of Economic Theory, Elsevier, Elsevier, vol. 79(2), pages 224-244, April.
  14. Wooders, Myrna, 1980. "The Tiebout Hypothesis: Near Optimality in Local Public Good Economies," Econometrica, Econometric Society, Econometric Society, vol. 48(6), pages 1467-85, September.
  15. Ray, Debraj & Vohra, Rajiv, 1997. "Equilibrium Binding Agreements," Journal of Economic Theory, Elsevier, Elsevier, vol. 73(1), pages 30-78, March.
  16. Conley, John P. & Wooders, Myrna H., 2001. "Tiebout Economies with Differential Genetic Types and Endogenously Chosen Crowding Characteristics," Journal of Economic Theory, Elsevier, Elsevier, vol. 98(2), pages 261-294, June.
  17. Martin Shubik, 1969. "The 'Bridge Game' Economy," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 267, Cowles Foundation for Research in Economics, Yale University.
  18. Hollard, Guillaume, 2000. "On the existence of a pure strategy Nash equilibrium in group formation games," Economics Letters, Elsevier, Elsevier, vol. 66(3), pages 283-287, March.
  19. Dieckmann, Tone, 1999. "The evolution of conventions with mobile players," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 38(1), pages 93-111, January.
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Cited by:
  1. 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.
  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. Page Jr., Frank H. & Wooders, Myrna, 2007. "Networks and clubs," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 64(3-4), pages 406-425.
  4. Ben Zissimos, 2010. "Why are Trade Agreements Regional?," Vanderbilt University Department of Economics Working Papers 1002, Vanderbilt University Department of Economics.

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