The dependency game: Multiperson reciprocal sharing leads to stable cooperation which can evolve into group formation

In the standard model for reciprocal collaboration, the repeated prisoner's dilemma (PD), it has proved difficult to establish collaboration in larger groups, necessitating the introduction of additional mechanisms such as reputation or assortedness. The problem is corroborated because current multiperson PDs model simultaneous player action, known as a common goods situation, whereas multiperson collaboration could be easier to obtain in a PD with alternate player action, a private goods situation. Here we present such a game, called a dependency game, and show that stable collaboration can be obtained in a 255 player simulation if only players are allowed to remember three previous benefactors, so they can play advanced tit-for-tat. Furthermore, we show that such a freely collaborating population is threatened by assorted strategies, which define groups that parasitize on independent tit-for-tat players. By excluding others, these groups engage in indirect reciprocal behaviour. Our model therefore combines many hitherto separate collaboration-enhancing concepts into one game, and suggests that group formation and collaboration are two separate social phenomena.