Cooperation for public goods poses a dilemma, where individuals are tempted to free ride on others' contributions. Classic solutions involve monitoring, reputation maintenance and costly incentives, but there are important collective actions based on simple and cheap cues only, for example unplanned protests and revolts. This can be explained by an Ising model with the assumption that individuals in uncertain situations tend to conform to the local majority in their network. Among initial defectors, noise such as rumors or opponents' provocations causes some of them to cooperate accidentally. At a critical level of noise, these cooperators trigger a cascade of cooperation. We find an analytic relationship between the phase transition and the asymmetry of the Ising model, which in turn reflects the asymmetry of cooperation and defection. This study thereby shows that in principle, the dilemma of cooperation can be solved by nothing more than a portion of random noise, without rational decision making.

中文翻译：

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公共产品自发合作

公共产品合作造成了两难境地，个人很容易搭上别人的贡献。经典的解决方案涉及监控、声誉维护和昂贵的激励措施，但也有一些重要的集体行动仅基于简单而廉价的线索，例如计划外的抗议和反抗。这可以通过 Ising 模型来解释，假设处于不确定情况下的个体倾向于遵守其网络中的局部多数。在最初的叛逃者中，谣言或对手的挑衅等噪音导致他们中的一些人意外合作。在临界噪音水平下，这些合作者会触发一连串的合作。我们发现相变与 Ising 模型的不对称性之间存在解析关系，这反过来又反映了合作和背离的不对称性。