Moran process in evolutionary game dynamics with interval payoffs and its application

Abstract

Moran process is an essential dynamic process of updating in stochastic evolutionary game dynamics for analyzing evolutionary game models with exact payoffs. The payoffs in the game are not crisp numbers because of how complicated and uncertain the environment is. Considering this problem, this work investigates the evolutionary game dynamics of Moran process with interval payoffs by using interval numbers to characterize the uncertainty in evolutionary games. Firstly, the interval fixation probability of the Moran process is derived under weak selection. Secondly, the conditions and the degrees of possibility for the dominant strategy in the population are calculated and the interval evolutionary equilibrium strategy is obtained. Then, the evolutionary game model under the prisoner’s dilemma is studied with the interval Moran process. Finally, the evolutionary process of the enterprise epidemic prevention strategy is studied with an evolutionary game model based on the interval Moran process. In addition, the influence of the uncertainty of local government regulation and public supervision on the choice of enterprise epidemic prevention strategies is analyzed by comparing numerical examples, and the superiority of the method in practical application is verified.