Evolution with Mutations Driven by Control Costs

Bergin and Lipman (1996) show that the refinement effect from the random mutations in the adaptive 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 these mutation rates as endogenously determined mistake probabilities, by assuming that players at some cost or disutility can control their mistake probability, i.e., the probability of implementing another pure strategy than intended. This is shown to corroborate the result in Kandori-Mailath-Rob and Young that the risk-dominant equilibrium is selected in 2 x 2-coordination games.