Arnold, Tone and Wooders, Myrna Holtz (2002) Dynamic club formation with coordination. Working Paper. University of Warwick, Department of Economics, Coventry.

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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.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	H Social Sciences > HB Economic Theory Q Science > QA Mathematics
Divisions:	Faculty of Social Sciences > Economics
Library of Congress Subject Headings (LCSH):	Equilibrium (Economics), Cooperation, Approximation theory, Functional analysis, Game theory
Series Name:	Warwick economic research papers
Publisher:	University of Warwick, Department of Economics
Place of Publication:	Coventry
Date:	May 2002
Number:	No.640
Number of Pages:	21
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/1550

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