Research on the resilience of reputation mechanism to the cooperative environment in the face of external shocks

Social development is changing rapidly, and the assumed stability of the cooperative environment is only an ideal state. In the majority of prior research concerning evolutionary games, it is commonly posited that external influences are absent, thereby allowing for an exclusive examination of the system’s intrinsic evolution. However, the situation in the real world is complex, dynamic, and unstable. Therefore, this paper proposes introducing an external shock that compels a change in the rate of cooperation during the evolutionary process. This approach aims to simulate environmental changes in the real world and to observe how these changes impact the rate of cooperation. When facing external shocks, the reputation mechanism has a certain degree of recovery ability, which provides certain support for the reputation theory. This paper also adds the mechanism of learning from historical strategies to the traditional reputation model, optimizing the resilience of the reputation mechanism in the face of external shocks. Simulation results show that history learning can promote the recovery of a cooperative environment faster and more stably, short memory length strengthens the role of temptation to defect, long memory amplifies the impact of the initial state, and the joint effect of history learning rate and memory length is complex.