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Dynamic Club Formation with Coordination

dc.contributor.authorArnold, Tone
dc.contributor.authorWooders, Myrna
dc.description.abstractWe 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.
dc.publisherVanderbilt Universityen
dc.subjectClub formation
dc.subjectbest-reply dynamics
dc.subjectNash club equilibrium
dc.subjectergodic Nash club equilibrium
dc.subjectJEL Classification Number: C72
dc.subjectJEL Classification Number: C73
dc.subjectJEL Classification Number: D62
dc.subjectJEL Classification Number: D71
dc.titleDynamic Club Formation with Coordination
dc.typeWorking Paperen

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