The impact of preferential selection mechanism based on average payoff and stability of payoff on the evolution of cooperation

Recent studies on memory-based cooperative evolution have focused on random selection of learning objects and only considered average payoff, neglecting stability of payoff. Here, we propose a preference selection mechanism adopting the TOPSIS method, a multi-attribute decision-making approach. We introduce the weighting factors ω1 and ω2, which refer to average payoff and stability of payoff, respectively. The probability that an individual select his neighbor is influenced by both average payoff and stability. We investigate the effect of memory length M and ω1 on the evolution of cooperation. The simulation results indicate that M and ω1 can both somewhat promote cooperation. Given that ω1 = ω2 = 0.5, for small betrayal temptation b, cooperation is more robust for small M, while for large b, large values of M are preferred. Further exploring the impact of ω1, for relatively small b, the influence of ω1 on cooperation is gradually revealed and strengthened as M increases. Conversely, for relatively large b, the impact of ω1 on cooperation slowly diminishes from strong as M increase, reflecting a gradual rise in the importance of stability. These findings enhance understanding of cooperative behavior in real social environments and make more rational decisions under the multi-factor evaluation based on average payoff and stability.