Social exclusion with dynamic cost on the evolution of cooperation in spatial public goods games

Social exclusion, as a special form of punishment, can effectively promote cooperation in spatial public goods game (SPGG). Previous research usually assumes that the unit cost of exclusion and the probability of exclusion success are statically fixed. As such, the total cost of an excluder can only be described as a linear function of the number of defectors. However, the scale return effect generally results in nonlinear characteristics of costs. In this study, we have thus relaxed the linear assumption and introduced a state-dependent kind of social exclusion with dynamic costs. Specifically, we describe the unit cost of exclusion as a function of the state of the group in which individuals are located. Due to the scale effect of punishment, an increase in the number of defectors in the group will result in a decrease in the unit cost of exclusion. We explore the impacts of this exclusion-type strategy in the SPGG with nonlinear exclusion cost on the evolution of cooperation. We further investigate parameters such as the cost parameter, the probability of exclusion success and the dilemma strength of the PGG on the evolution of cooperation. Simulations are performed on a square lattice with the traditional neighborhood structure and the Moore neighborhood structure, respectively. The results show that social exclusion with state-dependent costs can promote cooperation within a wide range of parameters in both cases. Especially, when the probability of exclusion success is high, a very strong dilemma strength can lead the system to form huge cooperative clusters to beat defectors. We further confirm that the Moore neighborhood case is more conducive to the evolution of cooperation in our social exclusion mechanism with dynamic cost compared with the traditional neighborhood case. These results allow us to better understand the role of the dynamic cost of punishment in the emergence of prosocial behavior.