Learning, mutation, and long run equilibria in games.

*(English)*Zbl 0776.90095Summary: 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 \(2\times 2\) symmetric games with two symmetric strict Nash equilibria the equilibrium selected satisfies (for large populations) the criterion of risk-dominance of J. C. Harsanyi and R. Selten [“A general theory of equilibrium selection in games” (1988; Zbl 0693.90098)]. In particular, if both strategies have equal security levels, the Pareto dominant Nash equilibrium is selected, even though there is another strict Nash equilibrium.

##### MSC:

91A15 | Stochastic games, stochastic differential games |

92D15 | Problems related to evolution |

91E40 | Memory and learning in psychology |