Evolution in Games with Endogenous Mistake Probabilities

JEL code: C72 keywords: evolution, mutation rates, mistakes ¤The authors are grateful for helpful comments from one referee and one associate editor of this journal, as well as from Sjaak Hurkens, Jens Josephson, Alexander Matros, Arthur Robson, Maria Saez-Marti and Philippe Solal, and participants at seminars at the London School of Economics, the EEA 1999 congress in Santiago di Compostela, and the ̄rst world congress of the Game Theory Society in Bilbao, 2000. This paper is a revised and condensed version of van Damme and Weibull (1999). Evolution in games with endogenous mistake probabilities 3 Running head: Endogenous mistake probabilities Proofs sent to: Eric van Damme Tilburg University, P.O. Box 90153 5000 LE Tilburg The Netherlands Abstract: Bergin and Lipman (1996) show that the selection e®ect from the random mutations in the adaptive population dynamics in Kandori, Mailath and Rob (1993) and Young (1993) is due to restrictions on how these mutation rates vary across population states. We here model mutation rates as endogenously determined mistake probabilities, by assuming that players with some e®ort can control the probability of implementing the intended strategy. This is shown to corroborate the results in Kandori-Mailath-Rob (1993) and, under certain regularity conditions, those in Young (1993). Bergin and Lipman (1996) show that the selection e®ect from the random mutations in the adaptive population dynamics in Kandori, Mailath and Rob (1993) and Young (1993) is due to restrictions on how these mutation rates vary across population states. We here model mutation rates as endogenously determined mistake probabilities, by assuming that players with some e®ort can control the probability of implementing the intended strategy. This is shown to corroborate the results in Kandori-Mailath-Rob (1993) and, under certain regularity conditions, those in Young (1993). Evolution in games with endogenous mistake probabilities 4