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.