No abstract

We characterize solutions of a class of time-homogeneous optimal control problems with semilinear running costs and state constraints as maximal viscosity subsolutions to Hamilton-Jacobi equations and show that optimal solutions to these problems can be constructed explicitly. We present applications to large deviations problems arising in evolutionary game theory.

No abstract

No abstract

The hawk-dove game admits two types of equilibria: an asymmetric pure equilibrium in which players in one population play "hawk" and players in the other population play "dove," and a symmetric mixed equilibrium. The existing literature on dynamic evolutionary models shows that populations will converge to playing one of the asymmetric pure equilibria from any initial state. By contrast, we show that plausible sampling dynamics, in which agents occasionally revise their actions by observing either opponents' behavior or payoffs in a few past interactions, can induce the opposite result: global convergence to a symmetric mixed equilibrium.

We study population dynamics under which each revising agent tests each strategy k times, with each trial being against a newly drawn opponent, and chooses the strategy whose mean payoff was highest. When k = 1, defection is globally stable in the prisoner's dilemma. By contrast, when k > 1 we show that there exists a globally stable state in which agents cooperate with probability between 28% and 50%. Next, we characterize stability of strict equilibria in general games. Our results demonstrate that the empirically-plausible case of k > 1 can yield qualitatively different predictions than the case of k = 1 that is commonly studied in the literature.

No abstract

No abstract