Dynamic punishment-reputation synergy drives cooperation in spatial public goods game

In general, individuals with high reputation often leverage greater access to resources, influence, and opportunities, creating a differential advantage in societal hierarchies. Meanwhile, real legal systems impose stricter punishments on severe crimes to ensure proportional justice. In some social contexts, individuals who engage in punishment behavior may be perceived as more trustworthy or committed to group norms, potentially leading to an enhanced reputation. Motivated by these real-world observations, we incorporate a mechanism combining dynamic probabilistic punishment and reputation-driven cost reduction into the spatial public goods game, aiming to investigate their collective impact on the evolution of cooperative behavior in populations. Through extensive simulation experiments, it is proved that the mechanism of dynamic probabilistic punishment and reputation merging effectively promotes the evolution of cooperation. Critically, a larger reputation increment is more conducive to the emergence and promotion of cooperation. Notably, increasing reputation increments reduce cooperation's critical threshold toward lower bounds, resolving cooperation dilemmas while enhancing reputation-based strategy adoption that promotes cooperative prosperity. Even when the punishment cost exceeds the imposed fine, it still facilitates cooperation evolution to some extent, while increasing the initial punishment probability significantly enhances cooperative engagement and accelerates evolutionary dynamics, though adjustments to the reputation threshold demonstrate negligible impact on cooperative evolution within the population. These findings could be beneficial in our understanding of the combined effects of reputation and punishment on the emergence of cooperation.