Evolution of cooperation in spatial public goods games with resource-allocating leaders

In reality, the unequal distribution of resources and the growing lack of trust have become increasingly prominent issues, making it essential to explore how a well-designed leadership system can enhance teamwork and address these challenges. To explore this topic comprehensively, we introduced leaders with the authority to allocate public resources in a spatial public goods game. We examine how various leader selection mechanisms, levels of authority, and resource allocation strategies influence the evolution of cooperative behavior. By adjusting the weight of reputation in the leader selection process, we compare three selection mechanisms: random selection, selection based on the proportion of reputation, and direct selection of the individual with the highest reputation, and find that greater influence of reputation in the leader selection process consistently leads to higher levels of group cooperation. Furthermore, we assign leaders varying power levels and further analyze the impact of power magnitude on cooperative behavior. Our findings reveal that different leader selection mechanisms correspond to distinct optimal ranges of power, within which the presence of a leader significantly lowers the thresholds for cooperation and stabilizes group cooperation. However, when a leader's power exceeds the optimal range, the excessive concentration of power can hinder cooperative behavior. Finally, by adjusting the proportion of resource allocation, we observe that allocation strategies favoring cooperators effectively improve their survival conditions, suppress free-riding behaviors, and further enhance group cooperation. These findings deepen our understanding of the role of leaders in multiplayer games, particularly regarding their selection mechanisms and magnitude of leader authority, while offering new theoretical insights for addressing dilemmas in multiplayer scenarios.