Emergence of Cooperation in Spatial Public Goods Games via Grey Wolf Optimization and a Reputation Mechanism

In public goods games, the core challenge to sustaining cooperation lies in overcoming the temptation for individuals to free-ride, thereby achieving a collective optimum. Classical spatial game models, which typically employ local imitationbased update rules (e.g., the Fermi rule) and discrete binary strategies, have provided a foundational basis for understanding this problem. To explore more complex cooperative dynamics, this study introduces a novel social learning paradigm. Drawing inspiration from the grey wolf optimization (GWO) algorithm, we abstract its mechanism of collaborative hunting by the leadership layer into an active learning process based on local exemplars, which aligns with the real-world behavior of emulating successful peers. This framework transcends the passive imitation of a single strategy; instead, it emphasizes an active learning process where agents identify and synthesize the leadership group within their social network to explore superior cooperative strategies. We further construct a composite fitness metric by integrating long-term reputation with immediate payoffs and adopt a continuous strategy space to enhance behavioral granularity. Numerical simulations demonstrate that this integrated framework—combining active learning, a reputation mechanism, and continuous strategies—significantly promotes the emergence and maintenance of cooperation under stringent conditions. This research not only presents an effective new model for resolving social dilemmas but also offers a more behaviorally realistic theoretical perspective for understanding the evolution of cooperation in complex systems.