Positive feedback in coordination games: stochastic evolutionary dynamics and the logit choice rule

We show that under the logit dynamics, positive feedback among agents (also called bandwagon property) induces evolutionary paths along which agents repeat the same actions consecutively so as to minimize the payoff loss incurred by the feedback effects. In particular, for paths escaping the domain of attraction of a given equilibrium—called a convention—positive feedback implies that along the minimum cost escaping paths, agents always switch first from the status quo convention strategy before switching from other strategies. In addition, the relative strengths of positive feedback effects imply that the same transitions occur repeatedly in the cost minimizing escape paths. By combining these two effects, we show that in an escaping transition from one convention to another, the least unlikely escape paths from the status quo convention consist of only the repeated identical mistakes of agents. Using our results on the exit problem, we then characterize the stochastically stable states under the logit choice rule for a class of non-potential games with an arbitrary number of strategies.