Stochastic Darwinian equilibria in small and large populations
成果类型：
Article
署名作者：
Stegeman, M; Rhode, P
署名单位：
University of North Carolina; University of North Carolina Chapel Hill; Virginia Polytechnic Institute & State University
刊物名称：
GAMES AND ECONOMIC BEHAVIOR
ISSN/ISSBN：
0899-8256
DOI：
10.1016/j.geb.2003.10.005
发表日期：
2004
页码：
171-214
关键词：
摘要：
We establish necessary and sufficient conditions for the stability of stochastic Darwinian dynamics in quadratic games. Each player's strategy adjusts through mutation and selection shocks, and stability is independent of the rates at which these shocks arrive. Given stability, we characterize the midpoint of the nondegenerate ergodic distribution. In small populations, some equilibria correspond to relative payoff maximization, but others are unanticipated by existing static concepts. In the large population limit of a finite population, the set of stable Nash equilibria strictly includes all equilibria stable under myopic best reply, but some strict Nash equilibria are highly unstable. The stability result shows, for the first time, that large finite populations converge to Nash play even if they do not understand the game and strategies are so numerous that most are never played. The large population stability condition is related to risk dominance and, separately, to the static CSS condition. (C) 2003 Elsevier Inc. All rights reserved.