Predicting transitions in cooperation levels from network connectivity

Networks determine our social circles and the way we cooperate with others. We know that topological features like hubs degree assortativity affect cooperation, cooperation is favoured if benefit of altruistic act divided by cost exceeds average number neighbours. However, a simple rule would predict transitions on an arbitrary network has not yet been presented. Here show unique sequence degrees in can be used to at which game parameters major shifts level expected, including phase from absorbing mixed strategy phases. use evolutionary prisoner's dilemma random scale-free networks demonstrate prediction, as well its limitations possible pitfalls. observe good agreements between predictions results obtained concurrent Monte Carlo methods for update strategies, thus providing fast estimate outcome dilemmas without need actually playing game.