Evolution of cooperation under a time-varying peer pressure model in complex networks

In this paper, based on the traditional prisoner's dilemma model, we introduce time-varying peer pressure and verify the enhancing effect of this time-varying peer pressure model on cooperation in different types of networks. We decompose peer pressure into two aspects: pressure intensity, reflecting the degree of punishment an individual receives due to strategy inconsistency with neighbors, and pressure sensitivity, indicating the likelihood of an individual being influenced by peer pressure, which can be regarded as an individual characteristic. Considering individuals' continuous development over time, it is possible for individual characteristics to change over time. Thus, we treat pressure sensitivity as a time-varying function in this paper and construct it based on the widely used Sigmoid function, taking into account the differences in sensitivity among different individual types. We apply the time-varying peer pressure model to Watts-Strogatz (WS) and Barabási-Albert (BA) networks and evaluate its effect from two aspects: the increase in the proportion of cooperators compared to the traditional prisoner's dilemma model, and the range of b within which there are still cooperators that can survive in the system. Overall, we find that the introduction of the time-varying peer pressure can more significantly enhance the evolution of cooperation in WS networks. Specifically, under the time-varying peer pressure model, the range of b that the system can withstand can be expanded to b≤1.95 in WS networks, and the range expands to b≤2.7 in BA networks, while the network scale is 100.