Dynamic Club Formation with Coordination
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.
|Date of creation:||Sep 2005|
|Date of revision:|
|Contact details of provider:|| Web page: http://www.vanderbilt.edu/econ/wparchive/index.html|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Slikker, M. & Dutta, B. & Tijs, S.H. & van den Nouweland, C.G.A.M., 2000. "Potential maximizers and network formation," Other publications TiSEM a4848315-a441-4d55-acde-9, Tilburg University, School of Economics and Management.
- Slikker, M. & Dutta, P.K. & van den Nouweland, C.G.A.M. & Tijs, S.H., 1998. "Potential Maximizers and Network Formation," Research Memorandum 758, Tilburg University, School of Economics and Management.
- 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.
- 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.
- Milchtaich, Igal & Winter, Eyal, 2002.
"Stability and Segregation in Group Formation,"
Games and Economic Behavior,
Elsevier, vol. 38(2), pages 318-346, February.
- 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.
When requesting a correction, please mention this item's handle: RePEc:van:wpaper:0522. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (John P. Conley)
If references are entirely missing, you can add them using this form.