Cooperation enhancement through a double-layer coupling mechanism with varying interaction radius in Prisoner’s Dilemma

The intricate interaction relationships among individuals in a population often require representation via multi-layer networks. The coupling between network layers and the strategy update rules of individuals within each layer are pivotal for promoting cooperation. In this paper, we explore a double-layer-network Prisoner's Dilemma model. By incorporating a variable-radius interaction community, we establish cross-layer coupling through influence propagation and apply distinct strategy update rules to each layer. In the upper layer, experienced agents update strategies using a reinforcement-learning-based Q-learning rule. In the lower layer, agents integrate both the reputation information from their same-layer interaction community and the experiential information from the upper-layer agents, subsequently updating strategies via the Fermi update rule. Simulations reveal that the reinforcement learning mechanism effectively fosters cooperation. Both the interaction radius and the reputation factor enhance cooperation frequency significantly, and a larger interaction radius accelerates the convergence to stable cooperation.