Abstract
We study the evolution of cooperation in the collective-risk social dilemma game, where the risk is determined by a collective target that must be reached with individual contributions. All players initially receive endowments from the available amount of common resources. While cooperators contribute part of their endowment to the collective target, defectors do not. If the target is not reached, the endowments of all players are lost. In our model, we introduce a feedback between the amount of common resources and the contributions of cooperators. We show that cooperation can be sustained only if the common resources are preserved but never excessively abound. This, however, requires a delicate balance between the amount of common resources that initially exist, and the amount cooperators contribute to the collective target. Exceeding critical thresholds in either of the two amounts leads to loss of cooperation, and consequently to the depletion of common resources.
Highlights
We study the evolution of cooperation in the collective-risk social dilemma game, where the risk is determined by a collective target that must be reached with individual contributions
We depart from this traditional setup by introducing a feedback between the amount of common resources and the amount cooperators contribute to the collective target
We assume that there exists a common resource, a non-empty pool, which provides an initial endowment to every player
Summary
We study the evolution of cooperation in the collective-risk social dilemma game, where the risk is determined by a collective target that must be reached with individual contributions. The public goods game requires that players decide simultaneously whether they wish to contribute to the common pool, i.e., to cooperate, or not. The collective-risk social dilemma game describes how the failure to reach a declared collective target can have severe long-term consequences. We wish to draw on this example and use it as motivation to propose a minimalist model for a proof of principle — namely that the excessive abundance of common resources may hinder the evolution of cooperation in the collective-risk social dilemma game. We present results that we have obtained on the square lattice, while results for several other interaction networks are summarized in the Supplementary Information that accompanies this paper
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