Which risk scenarios can drive the emergence of costly cooperation?

In collective risk dilemmas, cooperation prevents collective loss only when players contribute sufficiently. In these more complex variants of a social dilemma, the form of the risk curve is crucial and can strongly affect the feasibility of a cooperative outcome. The risk typically depends on the sum of all individual contributions. Here, we introduce a general approach to analyze the stabilization of cooperation under any decreasing risk curve and discuss how different risk curves affect cooperative outcomes. We show that the corresponding solutions can be reached by social learning or evolutionary dynamics. Furthermore, we extend our analysis to cases where individuals do not only care about their expected payoff, but also about the associated distribution of payoffs. This approach is an essential step to understand the effects of risk decay on cooperation.