The impact of a dynamic reward pool mechanism based on historical memory on the cooperative evolution of spatial public goods games

This paper proposes a spatial public goods game model incorporating a dual-pool coupling mechanism to explore how delayed gratification and resource accumulation influence cooperation. Unlike traditional instant allocation models, we introduce an independent reward pool where resources undergo nonlinear amplification over time and are distributed based on historical contribution records. Simulation results indicate that this mechanism significantly promotes cooperation, particularly in harsh environments where traditional cooperation approaches fail. We identify two distinct ecological roles for investors: acting as survivors that form defensive clusters in low-synergy conditions, and serving as symbiotic cores that support diverse communities in high-synergy conditions. The memory-based exclusivity barrier effectively resolves the waning-moon effect by preventing defectors from appropriating accumulated wealth. Furthermore, parametric analysis indicates that the system exhibits asymmetric robustness, being highly sensitive to resource multiplication efficiency and distribution ratios but tolerant to investment costs. These findings provide theoretical insights into the design of sustainable social incentive systems.