Game dynamics of emotion evolution based on the Moran process

In this paper, emotions are classified into four types, namely, respect for the strong, envying the strong, sympathy for the weak, and bullying the weak. The corresponding relationship between the four emotion types and the two behaviors of competition and cooperation is then defined. The payoff matrices of the game based on emotions are obtained and the evolutionary dynamics of the four emotion types in a finite population based on the Moran process are studied. Next, we derive the absorption probabilities of a 4×4 symmetric evolutionary game of the population. The influence of the payoff parameters and the natural selection intensity on the result of the group evolution are then analyzed. The calculations indicate that there are differences in the absorption probabilities of the four absorption states of the system. At a steady state, individuals of the types envying the strong and bullying the weak have the highest probability of occupying the entire population, and individuals of the type respect for the strong and sympathy for the weak have the lowest one. By comparing the level of cooperation and average payoffs at a steady state, we observe that the level of cooperation and average payoffs based on the proposed model are better than those of the prisoner's dilemma game with two behaviors. Therefore, emotional evolution can promote cooperation and achieve better group fitness.