Evolution of cooperation in multi-agent systems driven by reputation-based migration

Traditional reputation models often focus on binary evaluation systems or rely on the frequency of agent behaviors (cooperation or defection), which are insufficient to accurately capture the feedback and evaluation provided by opponents in real-world social settings. Therefore, we propose a reputation mechanism based on payoff evaluation, where reputation updates are regulated using the decay factor α. Meanwhile, agents update their strategies through Q-learning and use the Fermi rule to assess whether migration should occur, based on the environment’s current state. Using the prisoner’s dilemma game on a square lattice as a paradigm, our simulation results show that use of Q-learning for strategy updates enables the population to achieve a higher fraction of cooperation at lower population densities ρ. Additionally, the decay factor α influences both the size of the clusters within the population and the number of isolated nodes. Dilemma intensity and population density jointly regulate the non-monotonic effect of α on the fraction of cooperators. Specifically, under low dilemma intensity, this non-monotonic effect only occurs in cases of low population density; as the dilemma intensity gradually increases, this effect expands to both high and low population density cases; and when the dilemma intensity is relatively high, high population density reverts to a monotonic effect of α on the fraction of cooperators.