Replicator dynamics of public goods game with tax-based punishment

Punishment is a promising direction to cooperation and thus has been widely studied through evolutionary game theory , offering potential solutions to social dilemmas. As one of its applications in the real world, taxation could be a supporting mechanism for punishment. This study analyzes the replicator dynamics of the public goods game with tax-based punishment in an infinitely large, well-mixed population. The analysis results suggest that the combination of punishment and taxation can stabilize cooperation. Intriguingly, the results show that the tax-based punishment and the tax-based pure reward can have the same conditions for stabilizing the same cooperation level despite their completely opposite mechanisms. • Punishers can coexist with non-punishers in the public goods game with tax-based punishment. • The population share of punishers is determined by the tax and the punishment cost. • Whether contributors are dominant is determined by the synergy factor and the punishment fine. • Tax-based punishment and reward models can potentially achieve the same level of cooperation despite their completely opposite mechanisms.