Small world can alleviate the social dilemmas originating from self-regulation or community policing issues

Self-regulation and government regulation, community policing and external powerful forces, respectively, form vital part of today’s global economy and social management. The implementation of regulation from self-regulation or community policing requires considerable disciplined members to share the costs of execution, while government or external powerful forces are more likely to make an strong intervention as the industry or community is being widely eroded, which are thus two definitely different feedback regulation schemes. Together with those wrong-doers, the organizations of the two feedback regulation schemes consist of both first-order and novel second-order social dilemma. It still remains a significant challenge to identify an optimal structure to simultaneously alleviate the two dilemmas, and even to additionally favor the altruistic individuals. To address this issue, in this paper we adopt an evolutionary game model within the framework of the public good model, by considering defector-driven and cooperator-driven punishment to map the two feedback regulation schemes, respectively. Through a series of extensive Monte Carlo simulation experiments and mean-field analysis based on replicator dynamics, we finally uncover the combination of clustering and shortcuts, say the small-world structure, is required to largely alleviate both first-order and novel second-order dilemma, which can not only yield optimal public goods by successfully eliminating defectors through strong network reciprocity from dense local connections, but also provide sufficient shortcuts to promote the dominance of defector-driven punishers. Our findings can be beneficial for improving self-regulation or community policing systems by constructing novel monitoring networks.