Orders of limits for stationary distributions, stochastic dominance, and stochastic stability

• 成果类型: Article
• 署名作者: Sandholm, William H.
• 署名单位: University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1933-6837
• DOI: 10.3982/TE554
• 发表日期: 2010-01-01
• 页码: 1-26
• 关键词: Evolutionary game theory; stochastic stability; equilibrium selection

摘要

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 eta is small and the population size N is large. We obtain a precise characterization of the asymptotics of the stationary distributions mu(N,eta) as eta approaches zero and N approaches infinity, and we establish that these asymptotics are the same for either order of limits and for all simultaneous limits. In general, different noisy best response rules can generate different stochastically stable states. To obtain a robust selection result, 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.