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# The Statistical Mechanics of Best-Response Strategy Revision

## Author

Listed:
• Lawrence Blume

## 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.

## Suggested Citation

• Lawrence Blume, 1993. "The Statistical Mechanics of Best-Response Strategy Revision," Game Theory and Information 9307001, University Library of Munich, Germany, revised 26 Jan 1994.
• Handle: RePEc:wpa:wuwpga:9307001
Note: 29 pages, plain TeX with two tables, all macros included. This new version extends the results of the previous version to games with strategic complementarities and some other K x K games.
as

File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/9307/9307001.pdf

File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/9307/9307001.ps.gz

## References listed on IDEAS

as
1. Bergstrom, Theodore C, 1995. "On the Evolution of Altruistic Ethical Rules for Siblings," American Economic Review, American Economic Association, vol. 85(1), pages 58-81, March.
2. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
3. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
Full references (including those not matched with items on IDEAS)

### JEL classification:

• C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
• D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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