Excess payoff dynamics and other well-behaved evolutionary dynamics

• 成果类型: Article
• 署名作者: Sandholm, WH
• 署名单位: University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2005.02.003
• 发表日期: 2005
• 页码: 149-170
• 关键词: Evolutionary game theory; foundations for evolutionary dynamics; Nash equilibrium

摘要

We consider a model of evolution in games in which agents occasionally receive opportunities to switch strategies, choosing between them using a probabilistic rule. Both the rate at which revision opportunities arrive and the probabilities with which each strategy is chosen are functions of current normalized payoffs. We call the aggregate dynamics induced by this model excess payoff dynamics. We show that every excess payoff dynamic is well-behaved: regardless of the underlying game, each excess payoff dynamic admits unique solution trajectories that vary continuously with the initial state, identifies rest points with Nash equilibria, and respects a basic payoff monotonicity property. We show how excess payoff dynamics can be used to construct well-behaved modifications of imitative dynamics, and relate them to two other well-behaved dynamics based on projections. (c) 2005 Elsevier Inc. All rights reserved.