Abstract
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.
Highlights
In collective risk dilemmas, cooperation prevents collective loss only when players contribute sufficiently
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
Summary
Kristin Hagel1,*, Maria Abou Chakra2,*, Benedikt Bauer2 & Arne Traulsen[2] received: 18 September 2015 accepted: 26 November 2015. Social dilemmas arise when self-interested individuals have a conflict between their personal gain and the success of their group This leads to the ‘free-rider’ problem in the classical public good games[1,2]. The degree of risk attributed to the loss can affect the amount contributed by individual group members In this dilemma, the risk probability can play a major role in the decisions made[17,20,29,30]. The majority of studies has focused on the piecewise step level function, which was the original curve used in experiments[17] In such a strict setup, individuals are expected to contribute more for high risk probabilities than for low risk probabilities[17,18,19,20,21,22]. Strategies will be affected when players have preferences concerning the variation of the payoffs and not optimize their expected payoff
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