The impact of environmental disorder-induced constraints on spatial public goods games with social exclusion

Abstract

Social exclusion is a powerful strategy in spatial public goods games for fostering cooperation, but it comes with costs and limitations. Inspired by the Broken Windows theory, connecting disorderly environments to community breakdown, we present two environmentally constrained cases. One case limits exclusion by dynamic exclusion probability, while the other faces constraints based on the dynamic unit cost of exclusion. Our analysis studies the evolutionarily stable state and phase transition processes under various parameter spaces for both cases. Results show that cooperation is promoted widely in both scenarios. Interestingly, when the unit cost of exclusion is dynamic, there is a notable expansion in the parameter space, leading to complete cooperation. Despite disorderly environments, both exclusion strategies effectively promote cooperation, with the dynamic cost strategy outperforming the dynamic exclusion probability strategy. These findings enhance our understanding of how environmental constraints and social exclusion shape prosocial behaviors.