Sampling Dynamics and Stable Mixing in Hawk–Dove Games

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.