Fast convergence in evolutionary models: A Lyapunov approach

Evolutionary models in which N players are repeatedly matched to play a game G have fast convergenceto a set A if the models both reach A quickly and leave A slowly. where quicklyand slowly refer to whether convergence times remain nite in the N! 1 limit. We provide Lyapunov criteria which are su ¢ cient for reaching quickly and leaving slowly, and apply them to a number of examples which illustrate how they depend on the degree of risk-dominance in the game, noise levels, the nature of the decision rule, and the nature of the infomation on which players base their decisions.