Reporting is a double-edged sword for promoting cooperation in the public goods game

Reporting is widespread in human society, yet its theoretical mechanisms for cooperation in a monitored society remain unclear. Here, we introduce a reporting mechanism into the public goods game to investigate its impact on the emergence of cooperative behavior in a monitored environment. We analyze well-mixed populations and structured populations. Through theoretical analysis and numerical calculations, we find that when the fine is low, the introduction of the reporting mechanism effectively transforms the public goods game into a coordination game, thereby enhancing the feasibility of cooperation. Moreover, when the fine is high, cooperation emerges as a globally stable evolutionary strategy. Our results further indicate that reporting intensity exerts a nonlinear effect on public cooperation: moderate reporting intensity favors the evolution of cooperation, whereas excessive frequency or generosity in reporting may weaken its efficacy. Additionally, Monte Carlo simulation results on structured populations are consistent with those obtained in well-mixed populations. Notably, we observe a discontinuous phase transition in cooperation levels upon variation of reporting parameters, which can precipitate an outbreak of cooperation. These findings reveal reporting as a double-edged sword, emphasizing the need to balance its reporting parameters for optimal cooperation.