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.