Constructive agents nullify the ability of destructive agents to foster cooperation in public goods games

Existing studies have revealed a paradoxical phenomenon in public goods games, wherein destructive agents, harming both cooperators and defectors, can unexpectedly bolster cooperation. Building upon this intriguing premise, our paper introduces a novel concept: constructive agents, which confer additional benefits to both cooperators and defectors. We investigate the impact of these agents on cooperation dynamics within the framework of public goods games. Employing replicator dynamics, we find that unlike destructive agents, the mere presence of constructive agents does not significantly alter the defective equilibrium. However, when the benefits from constructive agents are outweighed by the damage inflicted by destructive agents, the addition of constructive agents does not affect the ability of destructive agents to sustain cooperation. In this scenario, cooperators can be maintained through a cyclic dominance between cooperators, defectors, and destructive agents, with constructive agents adding complexity but not fundamentally changing the equilibrium. Conversely, if the benefits from constructive agents surpass the harm caused by destructive agents, the presence of constructive agents nullifies the ability of destructive agents to foster cooperation. Our results highlight the nuanced role of constructive agents in cooperation dynamics, emphasizing the necessity of carefully assessing incentive balances when encouraging cooperation.