Evolution of collective action in adaptive social structures

Many problems in nature can be conveniently framed as a problem of evolution of collective cooperative behaviour, often modelled resorting to the tools of evolutionary game theory in well-mixed populations, combined with an appropriate N-person dilemma. Yet, the well-mixed assumption fails to describe the population dynamics whenever individuals have a say in deciding which groups they will participate. Here we propose a simple model in which dynamical group formation is described as a result of a topological evolution of a social network of interactions. We show analytically how evolutionary dynamics under public goods games in finite adaptive networks can be effectively transformed into a N-Person dilemma involving both coordination and co-existence. Such dynamics would be impossible to foresee from more conventional 2-person interactions as well as from descriptions based on infinite, well-mixed populations. Finally, we show how stochastic effects help rendering cooperation viable, promoting polymorphic configurations in which cooperators prevail.This research was supported by FCT-Portugal through grants PTDC/FIS/101248/2008 and PTDC/MAT/122897/2010, by multi-annual funding of CMAF-UL and INESC-ID (under the project PEst-OE/EEI/LA0021/2011) provided by FCT-Portugal. Partial Financial support by the National Science Foundation under Grant No. NSF PHY11-25915 is also gratefully acknowledged