Adaptive reward-punishment mechanism promotes the evolution of cooperation in public goods games via deep reinforcement learning

Carbon mitigation poses a substantial challenge during the course of industrialization. Evolutionary game theory offers a universal framework to examine the dynamic evolution of mitigation strategies across diverse agents, whereas the public goods game exposes the social dilemma triggered by “free-riding”. Reward-punishment mechanisms have been proven to be effective means to promote the collective cooperation, but prior studies on reward and punishment mechanisms in evolutionary game theory have frequently lacked the adaptability, rendering real-time dynamic optimization in complex systems difficult to achieve. Starting from the evolutionary game theory, we present a multi-agent decision-making framework for carbon emission governance that integrates deep reinforcement learning (DRL) and graph neural networks (GNN). In this work, we introduce a learning-enabled “social planner” agent within the population that dynamically adjusts strategies through node-level interventions (reward, punishment, no action) in complex network environments, which helps to promote the evolution of cooperative emission reduction behaviors. Numerical simulation results demonstrate that this mechanism can significantly improve the collective cooperation level, particularly when intervention intensity and reward weight are coordinately optimized. Meanwhile, the agent can autonomously identify key nodes in the network for targeted interventions and exhibits strong adaptability across different network topologies. Our work offers a novel theoretical perspective and scalable intelligent decision support for addressing the “free-riding” dilemma in the carbon emission governance.