SwissQuant Group AG, Kuttelgasse 7, 8001 Zurich, Switzerland.
Evolution. 2010 Aug;64(8):2458-65. doi: 10.1111/j.1558-5646.2010.00986.x. Epub 2010 Feb 26.
Related to the often applied cooperation models of social dilemmas, we deal with scenarios in which defection dominates cooperation, but an intermediate fraction of cooperators, that is, "partial cooperation," would maximize the overall performance of a group of individuals. Of course, such a solution comes at the expense of cooperators that do not profit from the overall maximum. However, because there are mechanisms accounting for mutual benefits after repeated interactions or through evolutionary mechanisms, such situations can constitute "dilemmas" of partial cooperation. Among the 12 ordinally distinct, symmetrical 2 x 2 games, three (barely considered) variants are correspondents of such dilemmas. Whereas some previous studies investigated particular instances of such games, we here provide the unifying framework and concisely relate it to the broad literature on cooperation in social dilemmas. Complementing our argumentation, we study the evolution of partial cooperation by deriving the respective conditions under which coexistence of cooperators and defectors, that is, partial cooperation, can be a stable outcome of evolutionary dynamics in these scenarios. Finally, we discuss the relevance of such models for research on the large biodiversity and variation in cooperative efforts both in biological and social systems.
与社会困境中经常应用的合作模式相关，我们处理的场景是背叛主导合作，但存在一部分合作者，即“部分合作”，这将最大限度地提高一群个体的整体表现。当然，这种解决方案是以合作者的利益为代价的，因为他们无法从整体最大值中受益。然而，由于存在互惠互利的机制，例如在重复互动或通过进化机制之后，这种情况可能构成“部分合作”的困境。在 12 个有序不同、对称的 2 x 2 游戏中，有三个（勉强考虑）变体是这些困境的对应物。虽然之前的一些研究调查了这些游戏的特定实例，但我们在这里提供了统一的框架，并简明扼要地将其与社会困境中合作的广泛文献联系起来。为了补充我们的论证，我们通过推导出在这些场景中，合作者和背叛者共存，即部分合作，可以是进化动力学稳定结果的条件，来研究部分合作的进化。最后，我们讨论了这些模型对于研究生物和社会系统中合作努力的大生物多样性和变化的相关性。
