On Evolutionarily Stable Strategies

Evolutionarily stable strategy (ESS) is an essential concept in the research of biological evolution. By putting ESS under a metric space framework, this paper proposes a relaxed definition of ESS which is more suitable for the investigation of finite evolutionary games (EGs), that is, the ESS with stability radius. Based on the new definition, stability and stabilization of EGs and EGs with control are studied respectively.