Nakamaru Mayuko, Dieckmann Ulf
Department of Value and Decision Science, Tokyo Institute of Technology, 2-12-1-W9-35, O-okayama, Meguro-ku, Tokyo 152-8552, Japan.
J Theor Biol. 2009 Mar 7;257(1):1-8. doi: 10.1016/j.jtbi.2008.09.004. Epub 2008 Sep 18.
Punishing defectors is an important means of stabilizing cooperation. When levels of cooperation and punishment are continuous, individuals must employ suitable social standards for defining defectors and for determining punishment levels. Here we investigate the evolution of a social reaction norm, or psychological response function, for determining the punishment level meted out by individuals in dependence on the cooperation level exhibited by their neighbors in a lattice-structured population. We find that (1) cooperation and punishment can undergo runaway selection, with evolution towards enhanced cooperation and an ever more demanding punishment reaction norm mutually reinforcing each other; (2) this mechanism works best when punishment is strict, so that ambiguities in defining defectors are small; (3) when the strictness of punishment can adapt jointly with the threshold and severity of punishment, evolution favors the strict-and-severe punishment of individuals who offer slightly less than average cooperation levels; (4) strict-and-severe punishment naturally evolves and leads to much enhanced cooperation when cooperation without punishment would be weak and neither cooperation nor punishment are too costly; and (5) such evolutionary dynamics enable the bootstrapping of cooperation and punishment, through which defectors who never punish gradually and steadily evolve into cooperators who punish those they define as defectors.
惩罚背叛者是稳定合作的重要手段。当合作和惩罚水平是连续的时候，个体必须采用合适的社会标准来定义背叛者并确定惩罚水平。在此，我们研究一种社会反应规范或心理反应函数的演变，该函数用于确定个体根据其在晶格结构群体中邻居所表现出的合作水平而施加的惩罚水平。我们发现：（1）合作和惩罚会经历失控选择，朝着增强合作和更苛刻的惩罚反应规范的进化相互强化；（2）当惩罚严格时，这种机制效果最佳，这样定义背叛者时的模糊性就小；（3）当惩罚的严格程度能与惩罚的阈值和严厉程度共同适应时，进化有利于对合作水平略低于平均水平的个体进行严格且严厉的惩罚；（4）当没有惩罚时合作会很薄弱且合作和惩罚成本都不太高时，严格且严厉的惩罚会自然进化并导致合作大幅增强；（5）这种进化动态能够实现合作和惩罚的自我强化，通过这种方式，从不惩罚的背叛者会逐渐且稳定地演变成会惩罚他们所定义的背叛者的合作者。
