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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. Ray, Debraj & Vohra, Rajiv, 1997. "Equilibrium Binding Agreements," Journal of Economic Theory, Elsevier, Elsevier, vol. 73(1), pages 30-78, March.
  2. 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.
  3. Glen Ellison, 2010. "Learning, Local Interaction, and Coordination," Levine's Working Paper Archive 391, David K. Levine.
  4. 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.
  5. 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.
  6. Igal Milchtaich & Eyal Winter, 2000. "Stability and Segregation in Group Formation," Discussion Paper Series, The Center for the Study of Rationality, Hebrew University, Jerusalem dp263, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  7. Kovalenkov, Alexander & Wooders, Myrna Holtz, 1999. "Approximate Cores Of Games And Economies With Clubs," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 535, University of Warwick, Department of Economics.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. Dieckmann, Tone, 1999. "The evolution of conventions with mobile players," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 38(1), pages 93-111, January.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
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Citations

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Cited by:
  1. Ben Zissimos, 2011. "Why are Trade Agreements Regional?," Review of International Economics, Wiley Blackwell, Wiley Blackwell, vol. 19(1), pages 32-45, 02.
  2. Page Jr., Frank H. & Wooders, Myrna, 2009. "Strategic basins of attraction, the path dominance core, and network formation games," Games and Economic Behavior, Elsevier, Elsevier, vol. 66(1), pages 462-487, May.
  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. Frank H. Page, Jr. & Myrna H. Wooders, 2005. "Club Formation Games with Farsighted Agents," Vanderbilt University Department of Economics Working Papers, Vanderbilt University Department of Economics 0529, Vanderbilt University Department of Economics.

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