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Evolution Through Imitation in a Single Population

David K. Levine and Wolfgang Pesendorfer

September 29, 1999

revised: May 9, 2000

Abstract: Kandori, Mailath and Rob [1993] and Young [1993] showed how introducing random innovations into a model of evolutionary adjustment enables selection among Nash equilibria. Key to this result is that poorly performing strategies may be introduced in sufficient numbers that they begin to perform well. We examine imitation as an alternative and more plausible propagation mechanism. If imitation is much more likely than innovation, it is significantly easier to compute long-run equilibrium. The long-run limit contains only pure strategies. Calculations can be made by comparing pairs of pure strategies to see how well they do against one another. A sufficient condition for a profile to be the unique long-run equilibrium is that it beat all others in pairwise contests. A number of examples are considered..