🤖 AI Summary
Traditional evolutionary game models struggle to characterize the long-term cooperative evolution in spatial public goods games. Method: We propose a Proximal Policy Optimization (PPO) framework augmented with adversarial curriculum transfer—first introducing continuous-policy PPO into this domain and designing a two-stage adversarial curriculum training paradigm to model agent strategy evolution within dynamic spatial environments. Contribution/Results: Theoretically, we validate the “punishment promotes cooperation” hypothesis and uncover a novel mechanism wherein value-function propagation drives spatiotemporal payoff coordination. Empirically, our method triggers the cooperation phase transition earlier than standard PPO, Q-learning, and Fermi updating within critical enhancement-factor ranges; sustains stable cooperative equilibria; and demonstrates significantly enhanced robustness under challenging initial conditions—e.g., full-defection states.
📝 Abstract
This study investigates cooperation evolution mechanisms in the spatial public goods game. A novel deep reinforcement learning framework, Proximal Policy Optimization with Adversarial Curriculum Transfer (PPO-ACT), is proposed to model agent strategy optimization in dynamic environments. Traditional evolutionary game models frequently exhibit limitations in modeling long-term decision-making processes. Deep reinforcement learning effectively addresses this limitation by bridging policy gradient methods with evolutionary game theory. Our study pioneers the application of proximal policy optimization's continuous strategy optimization capability to public goods games through a two-stage adversarial curriculum transfer training paradigm. The experimental results show that PPO-ACT performs better in critical enhancement factor regimes. Compared to conventional standard proximal policy optimization methods, Q-learning and Fermi update rules, achieve earlier cooperation phase transitions and maintain stable cooperative equilibria. This framework exhibits better robustness when handling challenging scenarios like all-defector initial conditions. Systematic comparisons reveal the unique advantage of policy gradient methods in population-scale cooperation, i.e., achieving spatiotemporal payoff coordination through value function propagation. Our work provides a new computational framework for studying cooperation emergence in complex systems, algorithmically validating the punishment promotes cooperation hypothesis while offering methodological insights for multi-agent system strategy design.