The paper "Learning, Mutation, and Long Run Equilibria in Games" by Michihiro Kandori, George J. Mailath, and Rafael Rob analyzes an evolutionary model with a finite number of players and introduces mutations to perturb the system away from its deterministic evolution. The focus is on the implications of ongoing mutations, which reduce the set of equilibria to "long-run equilibria." For 2 × 2 symmetric games with two symmetric strict Nash equilibria, the equilibrium selected satisfies Harsanyi and Selten's (1988) criterion of risk-dominance. Specifically, if both strategies have equal security levels, the Pareto dominant Nash equilibrium is selected, even though there is another strict Nash equilibrium. The authors use a discrete framework to determine the most likely or long-run equilibrium and apply this to 2 × 2 coordination games, showing that the long-run equilibrium coincides with the risk-dominant equilibrium. The model is based on three hypotheses: inertia, myopia, and mutation, which describe boundedly rational behavior. The paper also discusses the robustness of the results and provides an informal discussion of the model, followed by a detailed mathematical formulation and analysis.The paper "Learning, Mutation, and Long Run Equilibria in Games" by Michihiro Kandori, George J. Mailath, and Rafael Rob analyzes an evolutionary model with a finite number of players and introduces mutations to perturb the system away from its deterministic evolution. The focus is on the implications of ongoing mutations, which reduce the set of equilibria to "long-run equilibria." For 2 × 2 symmetric games with two symmetric strict Nash equilibria, the equilibrium selected satisfies Harsanyi and Selten's (1988) criterion of risk-dominance. Specifically, if both strategies have equal security levels, the Pareto dominant Nash equilibrium is selected, even though there is another strict Nash equilibrium. The authors use a discrete framework to determine the most likely or long-run equilibrium and apply this to 2 × 2 coordination games, showing that the long-run equilibrium coincides with the risk-dominant equilibrium. The model is based on three hypotheses: inertia, myopia, and mutation, which describe boundedly rational behavior. The paper also discusses the robustness of the results and provides an informal discussion of the model, followed by a detailed mathematical formulation and analysis.