Reporting-triggered institutional incentives promote prosocial behaviors in networked public goods games.

The reporting phenomenon is ubiquitous in human society. However, how reporting-triggered institutional incentives influence public cooperation remains theoretically unresolved. Here, we construct a public goods game where individuals adopt one of three strategies: report, cooperate, and defect. In this game, cooperators and reporters contribute a cost to the common pool, whereas defectors make no contribution. Furthermore, each reporter pays a monitoring cost to detect defection and subsequently report it to the institution. Upon receiving a report, the institution will punish defectors and reward reporters with a response probability, irrespective of the number of reporters. We introduce the proposed game into a structured population and analytically derive the average fractions of cooperators, defectors, and reporters in the weak-selection limit by using the coalescing random walk method. We demonstrate that increasing the institutional response probability, reward intensity, or punishment intensity elevates the average fraction of reporters and reduces that of defectors, while keeping the average fraction of cooperators invariant. We further determine the conditions under which reporters are favored by natural selection, reporters are favored over cooperators, and contributors, including cooperators and reporters, prevail, respectively. We find that only when institutional incentives adequately offset the costs of contribution and monitoring can reporters gain an evolutionary advantage and contributors become dominant in the population. Notably, our main results remain robust under a group-dependent implementation rule, where the probability of implementing institutional incentives depends on the number of reporters in the group. Finally, these theoretical predictions are validated by numerical simulations.