A switching strategy between costly punishment and exclusion for the evolution of cooperation

Social exclusion and costly punishment have been regarded as potential measures to solve the conundrum of cooperation recently. In real life, what is pretty widespread is the combined use of multiple strategies. Here, we propose two different strategy switching rules, namely, peer switching and pool switching, to investigate the effect of conditional switching between punishment and exclusion on cooperation. We introduce the strategy switching threshold, thus switching institution depending on whether the number of defectors in the group exceeds the given switching threshold or not, can either exclude or punish free riders in the game. We show that switching threshold plays a decisive role in determining the evolutionary outcome. We reveal that a middle threshold value can stabilize the coexistence of cooperators, defectors, and strategy switching players in the population no matter whether pool-based or peer-based strategy switching rule is used. Particularly, compared with pure pool punishment and pure pool exclusion, pool strategy switching can better induce the stable coexistence state. Our results highlight the importance of conditional strategy switching for the supervision of public goods.