Dynamics and evolution of cooperation of the multiplayer snowdrift games on hypergraphs

We propose a Poor-Defect-Rich-Cooperation (PDRC) dynamic strategy and introduce it into a threshold-based multiplayer snowdrift game. A three-strategy framework, namely pure cooperation (C), pure defection (D), and Poor - Defect - Rich - Cooperation (PDRC), is constructed to investigate the dynamics of multi-strategy games and the evolution mechanism of cooperation on hypergraphs. By comparing with a two-strategy system containing only cooperation and defection, simulation results show that the introduction of the PDRC strategy significantly promotes the evolution of cooperation under specific parameters. In the two-strategy system, the defection strategy dominates and severely suppresses cooperation. In contrast, the three-strategy system eventually reaches a dynamic equilibrium dominated by the PDRC strategy, with the average group payoff and average cooperation rate being significantly higher than those of the two-strategy system. As the cooperator threshold decreases, the range of the cost-to-benefit ratio in which the three-strategy system outperforms the two-strategy system in terms of average cooperation level and average group payoff gradually expands. The PDRC strategy enhances the system's adaptability to low-threshold, low cost-to-benefit ratio environments. It can withstand the risk of collapse in high cost-to-benefit scenarios and avoid the complete collapse observed in the two-strategy system. The introduction of the negative cost mechanism does not change the cost-to-benefit ratio interval in which the three-strategy system outperforms the two-strategy system, but it leads to different evolutionary outcomes. The effect of negative cost is non-uniformly enhanced across different thresholds. The three-strategy system performs better at certain thresholds, and the strategy distribution exhibits richer evolutionary dynamics.