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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月18日

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  • Wei Tang,
  • Guoling Wang,
  • Zhiyan Xing

摘要

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.