Aspiration-driven strategy evolutionary dynamics under strong selection

Strategy update rules based on self-evaluation are very common in practice. Most of the previous studies on the update of aspiration-based self-evaluation strategies were based on the assumption that people’s adjustment intensity was low. Whether the successful propagation of human behavioral traits falls within this parameter is unclear. Therefore, it will be necessary to derive analytical results applicable to any selected intensity. In this paper, we focus on the effect of selection intensity on the level of population cooperation, and mainly focus on strong selection. We derive the results of the analysis for any selection intensity. The results show that under the condition of strong selection intensity, the evolution of cooperative strategy is strongly driven by aspiration, and significantly increase the cooperative strategy proportion compared with the results under weak selection. In addition, there is a critical cost-benefit ratio, which makes the proportion of cooperative strategy decrease sharply. The critical cost-benefit ratio decreases as the value of aspiration increase. However, when the selection intensity was weak, the aspiration value has a little effect on the proportion of cooperative strategies. We also reveal, essentially, the cause of the effect of aspiration value on the proportion of cooperative strategies at stable equilibrium time is the effect of aspiration value on the probability of strategy update under different configurations. In addition, the theoretical results are verified by Monte Carlo numerical simulation and the results are qualitatively consistent for different system sizes and structures. The apparent difference in the level of cooperation between strong and weak selection will be crucial to our basic understanding of human behavior and may lead to new insights into human self-evaluation. Graphic abstract