an:00279328
Zbl 0776.90095
Kandori, Michihiro; Mailath, George J.; Rob, Rafael
Learning, mutation, and long run equilibria in games
EN
Econometrica 61, No. 1, 29-56 (1993).
00011828
1993
j
91A15 92D15 91E40
bounded rationality; learning; Markov chains; equilibrium selection; evolutionary model; noise; mutations; symmetric strict Nash equilibria; risk-dominance
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 \textit{J. C. Harsanyi} and \textit{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.
Zbl 0693.90098