Effects of an update mechanism based on combinatorial memory and high-reputation learning objects on the evolution of cooperation

In human society, various factors influence decision-making, including memory, reputation, aspiration, etc. In recent years, research has increasingly focused on considering these factors and designing mechanisms to promote cooperation. However, few previous studies have simultaneously considered the effects of memory and reputation on cooperative evolution. Additionally, research on cooperation evolution based on memory mechanisms often focuses either on the strategy stability of the players themselves or on the strategy stability of the learning objects, but not both. Our study introduces an update mechanism based on combinatorial memory and high-reputation learning objects. This mechanism accounts for reputation and memory, where the memory effect includes the strategy stability of both the players and the learning objects. Specifically, at the stage of selecting learning objects, players prefer high-reputation individuals. We introduce a global selection weight, η, which allows players to select learning objects not only locally but also globally. At the stage of updating the strategy, each player simultaneously considers their own historical memory and the memory of their learning objects, with the parameter γ representing the memory weight of the learning objects. Monte Carlo simulations show that update rules that simultaneously consider both combinatorial memory and high-reputation learning objects are more effective in promoting cooperation than considering either factor alone. Furthermore, a small memory weight of the learning objects and a small global selection weight create an optimal environment for cooperation. Our study offers a novel approach to addressing social dilemmas and mitigating defection, emphasizing the critical roles of reputation and memory in the propagation of altruistic behavior.