Payoff Dependent Dynamics and Coordination Games

This paper considers populations of agents whose behavior when playing some underlying game is governed by perturbed best (or better) response dynamics with perturbation probabilities that depend log-linearly on payoffs, a class that includes the logit choice rule. A convention is a state at which every agent plays a strategy that corresponds to the same strict Nash equilibrium of the underlying game. For coordination games with zero payoffs off-diagonal, it is shown that the difficulty of leaving the basin of attraction of a convention can be well approximated by only considering paths of transitions on which an identical perturbation repeatedly affects one of the populations.