Mercenary punishment in structured populations

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