How group cohesion promotes the emergence of cooperation in public goods game under conditional dissociation?

Leaving is usually an option for individuals if they cannot tolerate their defective partners. In a two-player game, when a player chooses to leave, both she and her opponent become single players. However, in a multi-player game, the same decision may have different consequences depending on whether group cohesion exists. Players who choose not to leave would still be united together rather than be separated into singletons if there is cohesion among them. Considering this difference, we study two leaving mechanisms in public goods games. In the first mechanism, every player would be single once any of the group members leaves. In the second, we assume group cohesion exists that members who don’t leave form a union. In our model, each player adopts a trigger strategy characterized by a threshold: she leaves if the number of defectors in her group exceeds the threshold. We find that under both mechanisms, when the expected lifespan of individuals is long enough, cooperators with zero tolerance toward defection succeed in the evolution. Moreover, when cohesion exists in groups, cooperation is better promoted because the cooperators have a higher chance to play together. That is, group cohesion facilitates positive assortment and therefore promotes cooperation.