Social exclusion with antisocial punishment in spatial public goods game

Abstract

In the spatial public goods game (SPGG), social exclusion is an effective strategy to quickly promote group cooperation. However, the second-order free riding occurs among cooperators who do not bear additional exclusion costs in the process of exclusion. To ensure that the exclusion strategy works while solving the second-order free-riding problem, we introduce an antisocial punishment strategy. The model employs four counterbalancing strategies: pure cooperators invest into the public pool; the defectors are the first-order free-riders of the cooperators; the excluders restrict the defectors from riding the cooperators with a certain probability, and the excluded defectors cannot share the benefits of the common pool; and the antisocial punishers punish the cooperators. Through the Monte Carlo simulations, we found that the cooperative excluders protected the cooperators from invasion by defectors and defective punishers, and more importantly, the second-order free-riding problem of the system was eliminated by the defective punishers.