Evolutionary game dynamics of death-birth process with interval payoffs on graphs

Abstract

In this paper, we study the evolutionary game dynamics of the death-birth process with interval payoffs on graphs. First of all, we derive the interval replication dynamic equation. Secondly, we derive the fixation probability of the B-C prisoner’s dilemma game based on the death-birth process under the condition of weak selection, analyze the condition of the strategy fixed in the population, that is the condition of strategy A being dominant is analyzed. So we can judge whether natural selection is beneficial to strategy A in the game process through this condition. Finally, the feasibility of this method is verified by several examples.