When does immigration facilitate efficiency?

This paper adds to the growing literature on stochastic evolutionary models. These models can be characterised by small probability shocks or mutations which perturb the system away from its deterministic evolution, allowing it to move between equilibria over a long period of time. Much of the literature has concentrated on the result that, in the limit as the mutation rate approaches zero, the stationary distribution becomes concentrated on the risk-dominant equilibrium because it is easier to flow into. However, it has been shown that in models of local interaction, allowing player movement eases the flow into the efficient equilibrium. This paper looks at the consequences of such player movement when there are capacity constraints which limit the number of agents who can reside at each location. The system may then settle into a mixed state in which different locations coordinate on different equilibria.