The evolution of cooperation in the Prisoner’s Dilemma and the Snowdrift game based on Particle Swarm Optimization

Abstract

This paper studies the evolution of cooperation in the Prisoner’s Dilemma (PD) and the Snowdrift (SD) game on a square lattice. Each player interacting with their neighbors can adopt mixed strategies describing an individual’s propensity to cooperate. Particle Swarm Optimization (PSO) is introduced into strategy update rules to investigate the evolution of cooperation. In the evolutionary game, each player updates its strategy according to the best strategy in all its past actions and the currently best strategy of its neighbors. The simulation results show that the PSO mechanism for strategy updating can promote the evolution of cooperation and sustain cooperation even under unfavorable conditions in both games. However, the spatial structure plays different roles in these two social dilemmas, which presents different characteristics of macroscopic cooperation pattern. Our research provides insights into the evolution of cooperation in both the Prisoner’s Dilemma and the Snowdrift game and maybe helpful in understanding the ubiquity of cooperation in natural and social systems.