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Learning, mutation, and long run equilibria in games. (English) Zbl 0776.90095
Summary: 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.

91A15 Stochastic games, stochastic differential games
92D15 Problems related to evolution
91E40 Memory and learning in psychology
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