Collaboration leads to cooperation on sparse networks

For almost four decades, cooperation has been studied through the lens of the prisoner’s dilemma game, with cooperation modelled as the play of a specific strategy. However, an alternative approach to cooperative behavior has recently been proposed. Known as collaboration, the new approach considers mutualistic strategic choice and can be applied to any game. Here, we bring these approaches together and study the effect of collaboration on cooperative dynamics in the standard prisoner’s dilemma setting. It turns out that, from a baseline of zero cooperation in the absence of collaboration, even relatively rare opportunities to collaborate can support material, and robust, levels of cooperation. This effect is mediated by the interaction structure, such that collaboration leads to greater levels of cooperation when each individual strategically interacts with relatively few other individuals, matching well-known characteristics of human interaction networks. Conversely, collaboratively induced cooperation vanishes from dense networks, thus placing environmental limits on collaboration’s successful role in cooperation.Author summary: It is traditional in game theory to model cooperation as the play of a given strategy in a social dilemma. This approach is subject to the criticism that cooperation has to be separately defined for each new situation in which it is considered. Recently, collaboration—the ability to participate in collective decision making and optimization, has been proposed as an alternative approach to cooperative behavior. Collaboration has the benefit that it can be defined independently of any game. We bring these two approaches together, showing that even relatively rare opportunities for collaboration can support robust levels of cooperation, especially when interaction networks are sparse. This result is significant as human networks are often sparse and so our results support the wide distribution and persistence of cooperation across human populations.