The impact of historical-behavior-based asymmetric reputation and deposit mechanisms on the evolutionary spatial public goods game.

In the context of interpersonal interactions in human society, reputation serves as an important indicator for evaluating an individual's behavior. Typically, low-reputation individuals are required to face additional constraints before taking certain actions. Moreover, an individual's reputation often exhibits asymmetric dynamics: trust is difficult to build but can be lost instantly. Therefore, this paper proposes a novel spatial public goods game model that integrates historical-behavior-based asymmetric reputation with a deposit mechanism. In this model, the growth or decay of individual reputation is modeled using distinct functions based on the number of consecutive rounds an individual maintains cooperation or defection. Low-reputation individuals are required to pay a deposit into the investment pool before the game; cooperators can reclaim this deposit as a reward, while defectors forfeit it. Simulation results show that the deposit mechanism serves as a powerful driver of cooperation, significantly reducing the critical enhancement factor required for the emergence of cooperation. The reputation threshold plays a crucial role in the evolution of cooperation: moderately increasing the threshold effectively promotes cooperation but exhibits a pronounced diminishing marginal effect. Adjusting the sensitivity of reputation to historical behavior also notably influences group cooperation levels. Furthermore, comprehensive analyses through heatmaps, snapshots, and other graphical data reveal that deposit amounts and reputation thresholds are the two core prerequisites for the emergence of cooperation. Their combined effects ultimately drive the realization of global cooperation.