Second-Order Reputation Promotes Cooperation in the Spatial Prisoner’s Dilemma Game

Abstract

Reputation can significantly improve the level of cooperation in human societies. In recent years, most research efforts considered binary image scores or first-order evaluation models, and second-order criteria were considered only in well-mixed populations. In this paper, we therefore study the impact of four typical second-order reputation evaluation models in the spatial prisoner's dilemma game. Second-order reputation evaluation entails that an individual's image score is updated not only in accordance with his own strategy, but also in accordance with the reputation of the neighbors. We introduce a value for the reputation step length such that individuals can only maximize their reputation if they cooperate with the surrounding high-reputation individuals, and then thus become influential individuals in the population. By means of systematic Monte Carlo simulations, we show that all four rules promote cooperation beyond spatial reciprocity in the considered prisoner's dilemma game, and we also show that the longer the reputation step length the higher the level of cooperation. These results shed light on how reputation in structured populations affects cooperative behavior, and they might have important implications for human group dynamics and for cooperation in human societies in general.