Evolution of Equilibria in the Long Run: A General Theory and Applications

Abstract

We extend the evolutionary process studied in Kandori et al., Econometrica 61 (1933), 29-56 to n × 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. Journal of Economic Literature Classification Numbers: C63, C72, D43.

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