Stochastic stability in asymmetric binary choice coordination games.

Mathias Staudigl

Abstract: A recent literature in evolutionary game theory is devoted to the question of robust equilibrium selection under noisy best-response dynamics. In this paper we present a complete picture of equilibrium selection for asymmetric binary choice coordination games in the small noise limit. We achieve this by transforming the stochastic stability analysis into an optimal control problem, which can be solved analytically. This approach allows us to obtain precise and clean equilibrium selection results for all canonical noisy best-response dynamics which have been proposed so far in the literature, among which we find the best-response with mutations dynamics, the logit dynamics and the probit dynamics. Highlights ► We study equilibrium selection in asymmetric binary choice coordination games. ► The evolutionary dynamics belongs to the family of noisy best-response dynamics. ► We develop the optimal control approach to evolutionary equilibrium selection. ► With this method we compute the stochastic potential of equilibria exactly. ► We apply this to the best-response with mutations, logit and probit dynamics.