Department of Organismic and Evolutionary Biology, Harvard University, 26 Oxford Street, Cambridge, Massachusetts 02138, USA.
Evolution. 2011 Apr;65(4):1140-8. doi: 10.1111/j.1558-5646.2010.01185.x. Epub 2010 Dec 1.
The production of public goods by the contribution of individual volunteers is a social dilemma because an individual that does not volunteer can benefit from the public good produced by the contributions of others. Therefore it is generally believed that public goods can be produced only in the presence of repeated interactions (which allow reciprocation, reputation effects and punishment) or relatedness (kin selection). Cooperation, however, often occurs in the absence of iterations and relatedness. We show that when the production of a public good is a Volunteer's Dilemma, in which a fixed number of cooperators is necessary to produce the public good, cooperators and defectors persist in a mixed equilibrium, without iterations and without relatedness. This mixed equilibrium is absent in the N-person Prisoner's Dilemma, in which the public good is a linear function of the individual contributions. We also show that the Prisoner's Dilemma and the Volunteer's Dilemma are the two opposite extremes of a general public goods game, and that all intermediate cases can have a mixed equilibrium like the Volunteer's Dilemma. The coexistence of cooperators and defectors, therefore, is a typical outcome of most social dilemmas, which requires neither relatedness nor iterations.
个体志愿者对公共物品的贡献所产生的公共物品生产是一种社会困境，因为不参与志愿服务的个体可以从他人贡献产生的公共物品中受益。因此，人们普遍认为，只有在存在重复互动（允许相互作用、声誉效应和惩罚）或关联性（亲缘选择）的情况下，公共物品才能产生。然而，合作经常在没有迭代和关联性的情况下发生。我们表明，当公共物品的生产是一个“志愿者困境”时，即需要一定数量的合作者来生产公共物品，那么合作者和叛徒会在一个混合的均衡中持续存在，而不需要迭代，也不需要关联性。在 N 人囚徒困境中，不存在这种混合均衡，其中公共物品是个人贡献的线性函数。我们还表明，囚徒困境和志愿者困境是一般公共物品博弈的两个极端，所有中间情况都可能像志愿者困境一样存在混合均衡。因此，合作者和叛徒的共存是大多数社会困境的典型结果，这既不需要关联性，也不需要迭代。
