Mercenary punishment in structured populations

TL;DR

This paper explores mercenary punishment strategies in structured populations, analyzing how different costs and tax levels influence cooperation, defection, and the stability of punishment mechanisms in social dilemmas.

Contribution

It introduces a model of mercenary punishment with tax-based funding, revealing how cost and tax levels affect the coexistence of strategies and overall cooperation.

Findings

Cyclic dominance emerges at negligible tax levels.

High tax levels eliminate the cyclic dominance.

Optimal cooperation occurs at intermediate punishment costs.

Abstract

Punishing those who refuse to participate in common efforts is a known and intensively studied way to maintain cooperation among self-interested agents. But this act is costly, hence punishers who are generally also engaged in the original joint venture, become vulnerable, which jeopardizes the effectiveness of this incentive. As an alternative, we may hire special players, whose only duty is to watch the population and punish defectors. Such a policelike or mercenary punishment can be maintained by a tax-based fund. If this tax is negligible, a cyclic dominance may emerge among different strategies. When this tax is relevant then this solution disappears. In the latter case, the fine level becomes a significant factor that determines whether punisher players coexist with cooperators or alternatively with defectors. The maximal average outcome can be reached at an intermediate cost value of punishment. Our observations highlight that we should take special care when such kind of punishment and accompanying tax are introduced to reach a collective goal.