Nonlinear Dynamics of Evolutionary Public Goods Games with Consistent- and Inconsistent-Moral-Standard Exclusive Sanctions

This paper investigates the evolution of public cooperation within a four-strategy public goods game that incorporates both consistently and inconsistently moralistic exclusion mechanisms. Using replicator dynamics in an infinite well-mixed population, we demonstrate that the presence of Inconsistent Moralists (IMs), i.e., non-contributors who hypocritically exclude other defectors, fundamentally reshapes the dynamical structure of the multi-player social dilemma game. While the system admits no interior fixed point and the IM strategy itself is evolutionarily unstable, IM acts as a critical catalyst by destabilizing pure defection and redirecting evolutionary trajectories toward exclusion-based cooperation. Ultimately, these findings reveal that diverse enforcement strategies can qualitatively alter evolutionary outcomes by providing a previously overlooked indirect pathway for cooperation to emerge and persist in social dilemmas.