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Evolution of equilibria in the long run: A general theory and applications. (English) Zbl 0837.90139
Summary: We extend the evolutionary process studied by M. Kandori, G. J. Mailath and the second author [Econometrica 61, No. 1, 29-56 (1993; Zbl 0776.90095)] to $$n\times n$$ games. The evolutionary process is driven by two forces: players switching to the best response against the present strategy configuration, and players experimenting with new strategies. We show that a unique behavior pattern, called the long-run equilibrium, arises even if the underlying game has multiple (static) equilibria. The paper gives a general algorithm for computing the LRE, and then applies it to two classes of economic games. For games of pure coordination, the LRE is the Pareto-efficient equilibrium. For games with strategic complementarities, the geometry of the best-response correspondence helps identify the LRE.

##### MSC:
 91A20 Multistage and repeated games 91E40 Memory and learning in psychology 92D15 Problems related to evolution
##### Keywords:
evolutionary process; long-run equilibrium
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