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

Abstract

International audienceIn 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 threathened 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

Bet hedging based cooperation can limit kin selection and form a basis for mutualism

“…From Fig. 2A and earlier work (Uitdehaag, 2009), it is evident that this strategy evolutionarily dominates more freely sharing strategies (share-with-all), confirming the dominance of kin selection.…”

“…Whereas the alternate sharing in the bet hedging model can be modelled by the alternate PD (Nowak and Sigmund, 1994), this new situation is now based on the simultaneous sharing of different resources, and can be modelled by the simultaneous PD (Axelrod and Hamilton, 1981). Both forms of PD have been shown to favour similar strategies (Frean, 1991;Nowak and Sigmund, 1994;Uitdehaag, 2009). For the 'simultaneous' mutualism, any deviations from the ideal nutrient spectrum could be captured in a variance, which would be a measure for the growth-retarding effects of a suboptimal nutrient supply.…”

“…To further show that bet hedging is a basis for cooperation, a previously published computational model was adapted (Uitdehaag, 2009), in which a population plays an alternate repeated PD game (Trivers, 1971). In this model, the cooperative tit-for-tat strategy (Axelrod and Hamilton, 1981) is evolutionarily stable if players are allowed to remember, and preferentially share with, players who previously shared with them.…”

“…For example population members can be a mixture of lean and muscular people. Now let's show how kin selection can dominate in the above population (see also Uitdehaag, 2009). Suppose that a mutant altruistic gene arises in a carrier of the muscularity allele M. This mutant is more self-selecting and induces players to share only with other muscular people (carriers of M).…”

“…A related partner brings the inherent genetic advantages of kin selection, but a non-related partner can be preferred if she gives access to exclusive resources. However, in previous simulations without any special benefit for mutualism (Uitdehaag, 2009), a tag-based strategy was allowed in a group of freely sharing tit-for-tat players. This resulted in tag-carriers exploiting the untagged players until the latter were extinct.…”