Evolution of cooperation guided by the coexistence of imitation learning and reinforcement learning

Promoting cooperation remains a major challenge in natural science. While most studies focus on single strategy update rules, individuals in real-life often use multiple strategies in response to dynamic environments. This paper introduces a mixed update rule combining imitation and reinforcement learning (RL). In imitation learning (IL), individuals adopt strategies from higher-payoff opponents, while RL relies on personal experience. Simulations of the Prisoner's Dilemma Game (PDG), Coexistence Game (CG), and Coordination Game (CoG), both in well-mixed populations and square lattice networks, show that: (i) cooperation and defection coexist in the PDG, resolving the dilemma of universal defection; (ii) cooperation exceeds the mixed Nash equilibrium in the CG; and (iii) cooperators dominate in the CoG. The mixed update rule outperforms single strategy approaches in those games, highlighting its effectiveness in fostering cooperation.