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The Statistical Mechanics of Best-Response Strategy Revision

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  • Blume Lawrence E.

Abstract

I continue the study, begun in Blume (1993), of stochastic strategy revision processes in large player populations where the range of interaction between players is small. Each player interacts directly with only a finite set of neighbors, but any two players indirectly interact through a finite chain of direct interactions. The purpose of this paper is to compare local strategic interaction with global strategic interaction when players update their choice according to the (myopic) best-response rule. I show that randomizing the order in which players update their strategic choice is sufficient to achieve coordination on the risk-dominant strategy in symmetric $2\times 2$ coordination games. The ``persistant randomness'' which is necessary to achieve similar coordination when the range of interaction is global is replaced by spatial variation in choice in the initial condition when strategic interactions are local. An extension of the risk-dominance idea gives the same convergence result for $K\times K$ games with strategic complementarities. Similar results for $K\times K$ pure coordination games and potential games are also presented.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 11 (1995)
Issue (Month): 2 (November)
Pages: 111-145

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Handle: RePEc:eee:gamebe:v:11:y:1995:i:2:p:111-145

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Web page: http://www.elsevier.com/locate/inca/622836

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  1. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  2. Glen Ellison, 2010. "Learning, Local Interaction, and Coordination," Levine's Working Paper Archive 391, David K. Levine.
  3. Theodore C. Bergstrom, . "On the Evolution of Altruistic Ethical Rules for Siblings," ELSE working papers 017, ESRC Centre on Economics Learning and Social Evolution.
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