Dynamic Club Formation with Coordination

Tone Arnold () and Myrna Wooders
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Tone Arnold: Department of Economics, University of Hohenheim

No 522, Vanderbilt University Department of Economics Working Papers from Vanderbilt University Department of Economics

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.

Keywords: Club formation; cooperation; best-reply dynamics; Nash club equilibrium; ergodic Nash club equilibrium (search for similar items in EconPapers)
JEL-codes: C72 C73 D62 D71 (search for similar items in EconPapers)
Date: 2005-09
New Economics Papers: this item is included in nep-gth
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Citations: View citations in EconPapers (9)

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http://www.accessecon.com/pubs/VUECON/vu05-w22.pdf First version, 2005 (application/pdf)

Related works:
Working Paper: Dynamic Club Formation with Coordination (2002)
Working Paper: DYNAMIC CLUB FORMATION WITH COORDINATION (2002)
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Persistent link: https://EconPapers.repec.org/RePEc:van:wpaper:0522

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