On the Co-Existence of Conventions

Recent stochastic evolutionary models have shown that the most likely convention when the probability of a mutation is sufficiently small is coordination on the risk-dominant strategy rather than the payoff-dominant one. This paper looks at the consequences of player movement between locations when there are constraints which limit the number of agents who can reside at each location. If the constraints are strong then the risk-dominance result continues to hold. However, we show that when sufficient movement is possible, the most likely outcome involves a mixed state in which agents at different locations coordinate on different strategies. In the asymmetric case, it is the location with the stronger constraint, limiting movement, that coordinates on the payoff-dominant strategy.