The selective imitation based on influence mechanism in evolutionary dynamics of the Prisoner’s dilemma game

Abstract

In this paper, we propose a novel influence mechanism and investigate the evolutionary dynamics of the Prisoner’s Dilemma on a square-lattice network. Participants are categorized as influential and ordinary groups based on a predetermined ratio, with their influence measured by a weighted sum of payoffs and reputation. Different from the assumption of random imitation in the existing research, we posit that participants, referred to as focal players, are more likely to imitate influential individuals. We use an improved Fermi function to calculate the probability of this strategic imitation. The simulation results indicate that the distribution of weights for influence values, the proportion of influential players, and the probability of influential participants selected by focal players all significantly influence the frequency of cooperation. Among these factors, the probability of selecting influential players serves as the primary determinant. This study presents a novel analytical methodology to exploit the impact of influential individuals in order to augment group cooperation within real-world scenarios.