Learning, Mutation, and Long Run Equilibria in Games

We analyze an evolutionary model with a finite number of players and with noise or mutations.The expansion and contraction of strategies is linked-as usual-to their current relative success, but mutations-which perturb the system away from its deterministic evolution-are present as well.Mutations can occur in every period, so the focus is on the implications of ongoing mutations, not a one-shot mutation.The effect of these mutations is to drastically reduce the set of equilibria to what we term "long-run equilibria."For 2 x 2 symmetric games with two symmetric strict Nash equilibria the equilibrium selected satisfies (for large populations) Harsanyi and Selten's (1988) criterion of risk-dominance.In particular, if both strategies have equal security levels, the Pareto dominant Nash equilibrium is selected, even though there is another strict Nash equilibrium.