Effect of Spatial Structure on the Evolution of Cooperation in the N-Choice Iterated Prisoner’s Dilemma

Abstract

The evolution of cooperation is an enduring conundrum in biology and the social sciences. The prisoner’s dilemma game has emerged as the most promising mathematical metaphors to study cooperation. Mechanisms promoting the evolution of cooperation in two-player, two-strategy spatial iterated prisoner’s dilemma (IPD) games have been discussed in great detail over the past decades. Understanding the effects of repeated interactions in n-choice spatial IPD game is a formidable challenge. In this paper, the simulations are conducted with four different types of neighbourhood structures, and agents update their strategies by probabilistically imitating the strategies of better performing neighbours. During the evolution each agent can modify his own strategy and/or personal feature via a particle swarm optimization approach in order to improve his utility. The particle swarm optimization (PSO) approach is a bionic method which can simulate the interactions among agents in a realistic way. The results show that the evolutionary stability of cooperation does emerge in n-choice spatial IPD game, and the consideration of social cohesion in PSO approach promotes the evolution of cooperation. In addition, the neighbourhood structures and cost-to-benefit ratio increase the capability of cooperation and prevent the invading of defectors.