Stable mixing in Hawk–Dove Games under best experienced payoff dynamics

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, in which hawks are frequently matched against each other. The existing literature shows that when two populations of agents are randomly matched to play the hawk–dove game, then there is convergence to one of the pure equilibria from almost any initial state. By contrast, we show that plausible dynamics, in which agents occasionally revise their actions based on the payoffs obtained in a few trials, often give rise to the opposite result: convergence to one of the interior stationary states.