Abstract:

Over the past 30 years, evolutionary game theory and the concept of an evolutionarily stable strategy (ESS) have been not only extensively developed and successfully applied to explain the evolution of animal behaviors, but also widely used in molecular biology, economics, politics and social sciences. However, the stochastic dynamical properties of evolutionary games in randomly fluctuating environments are still unclear. In this paper, we briefly introduce the concept of stochastic evolutionary stability (SES) that we recently proposed. The stochastic evolutionary stability not only extends the classic concept of the evolutionarily stably strategy but also provides a fundamental theoretical framework for understanding the evolutionary dynamics of animal behavior in a stochastic environment.

Key words: stochastic locally stability, stochastic evolutionary stability, stochastic convergence stability, random payoff