Inter-layer feedback mechanism with reinforcement learning boosts the evolution of cooperation in multilayer network

Cooperative dynamics are crucial in balancing individual and collective behaviors, with evolutionary game theory providing deep insights into this complex interplay. Complex social systems are often characterized by their multilayered structures, within which agents assume diverse roles, interacting and coupling through feedback, profoundly influencing each other across different domains. Given the efficacy of reinforcement learning in analyzing game-theoretic behaviors, we introduce a novel inter-layer feedback mechanism with self-adapting Q-learning algorithm, to explore the evolution of cooperative behaviors within multilayered network structures. One layer is named the classic layer, which comprises cooperators and defectors, while the other layer is named the management layer and contains punishers and inactive individuals. Based on self-adapting Q-learning, agents in management layer decide whether to choose punishment action through the proposed inter-layer feedback mechanism, which induces a game transition in the classic layer. The agents’ strategies in classic layer provide feedback to management layer’s agents and influence their strategy choices. Simulation results reveal that the lower punishment cost and greater punishment severity and reputation factors can facilitate the evolution of cooperation. Furthermore, the critical effect of the self-adapting Q-learning algorithm under the inter-layer feedback mechanism enables agents to engage in introspective learning, rather than mere imitation. Finally, the variations in the Q-value and state transition probabilities are explored that the inter-layer feedback mechanism incrementally increases the Q-value of cooperators over time, thereby augmenting the frequency of cooperation within the entire process from a microscopic perspective. This research aims to offer crucial insights into the dynamics of cooperative behavior within the social punishment dilemma through the perspectives of artificial intelligence.