Orders of Limits for Stationary Distributions, Stochastic Dominance, and Stochastic Stability
William H. Sandholm, University of Wisconsin, Madison
Abstract:
A population of agents recurrently plays a two-strategy population game. When an agent receives a revision opportunity, he chooses a new strategy using a noisy best response rule that satisfies mild regularity conditions; best response with mutations, logit choice, and probit choice are all permitted. We study the long run behavior of the resulting Markov process when the noise level is small and the population size is large. We obtain a precise characterization of the asymptotics of the stationary distributions, and we establish that these asymptotics are the same for either order of limits and for all simultaneous limits.
Finally, we introduce a refinement of risk dominance called stochastic dominance, and we prove that coordination on a given strategy is stochastically stable under every noisy best response rule if and only if that strategy is stochastically dominant.