How multilevel competition drives cooperation in stigmergic systems

Cooperation through stigmergy relies on reliable information left in a shared environment, yet individuals may benefit from misleading others. How competition within and between groups shapes this conflict remains unclear. We investigated this question using the Stigmer Game, in which human participants interact exclusively through ratings that modify a shared informational environment, under seven payment rules. Participants were classified as collaborators, neutrals or defectors. Between-group competition produced the highest collaboration, whereas within-group competition favoured defection. Adding between-group competition partly restored cooperation despite continued rivalry within groups, although this effect depended on reward distribution. A quantitative analysis showed that within-group and rank-based competitive pressures best described differences in behavioural composition across payment rules. A genetic algorithm further revealed distinct stationary strategy compositions under each payment rule that were largely independent of initial conditions and robust to perturbations. These results reproduced the opposing effects of between-group and within-group competition observed experimentally, while highlighting differences between immediate behavioural responses and the strategy distributions favoured by each rule's incentive structure. Defectors remained present under the mutation regime, illustrating the vulnerability of shared information to exploitation. Our findings show how the organization of competitive incentives shapes cooperation and information reliability in decentralized collective systems.