Bonus-based mercenary punishment promotes cooperation in public goods games

Various regions often adopt punish strategies to solve traffic congestion problems. Punishing defectors is an effective strategy to solve the first-order free-rider problem in a public goods game. But this behavior is costly because the punisher is often also involved in the original joint venture and therefore vulnerable, which jeopardizes the effectiveness of this incentive. As an option, we could hire special players whose sole duty would be to monitor the population and punish defectors. The fines collected by various regions will also be used to subsidize the construction of public transportation. Thereby, we derive inspiration, and propose an improved public goods game model based on bonus and mercenary punishment. Research has shown that after cooperator gives the punisher an appropriate bonus, cooperators can strengthen the punisher, thereby weakening the defector's advantage and indirectly promoting cooperation by stabilizing the punisher's position in the system. In addition, the mechanism of reusing the fines collected from defectors and then subsidize to other players in the system can directly promote the emergence of cooperation.