Social exclusion is widely used as a control mechanism to promote cooperative behavior in human societies. However, it remains unclear how such control strategies actually influence the evolutionary dynamics of cooperation. In this paper, we introduce two types of control strategies into a population of agents that play the public goods game, namely prosocial pool exclusion and antisocial pool exclusion, and we use the replicator equation to study the resulting evolutionary dynamics for infinite well-mixed populations.

We show that the introduction of prosocial pool exclusion can stabilize the coexistence of cooperators and defectors by means of periodic oscillations, but only in the absence of second-order prosocial pool exclusion. When considering also antisocial pool exclusion, we show that the population exhibits a heteroclinic circle, where cooperators can coexist with other strategists. Moreover, when second-order exclusion is taken into account, we find that prosocial pool exclusion is the dominant strategy, regardless of whether the second-order exclusion is prosocial or antisocial. In comparison with punishment, we conclude that prosocial pool exclusion is a more effective control mechanism to curb free-riding.

L. Liu, X. Chen, M. Perc, Evolutionary dynamics of cooperation in the public goods game with pool exclusion strategies, Nonlinear Dyn 97 749 (2019)