Lessard Sabin
Département de Mathématiques et de Statistique, Université de Montréal, C.P. 6128, Succursale Centre-ville, Montréal, Québec, Canada H3C 3J7.
Proc Biol Sci. 2007 Aug 7;274(1620):1861-5. doi: 10.1098/rspb.2007.0366.
In the context of the finitely repeated Prisoner's Dilemma with the possibility of cooperating or defecting each time, the strategy tit-for-tat (TFT) consists in cooperating the first time and copying the strategy previously used by the opponent the next times. Assuming random pairwise interactions in a finite population of always defecting individuals, TFT can be favoured by selection to go to fixation following its introduction as a mutant strategy. We deduce the condition for this to be the case under weak selection in the framework of a general reproduction scheme in discrete time. In fact, we show when and why the one-third rule for the evolution of cooperation holds, and how it extends to a more general rule. The condition turns out to be more stringent when the numbers of descendants left by the individuals from one time-step to the next may substantially differ. This suggests that the evolution of cooperation is made more difficult in populations with a highly skewed distribution of family size. This is illustrated by two examples.
在每次都有可能选择合作或背叛的有限重复囚徒困境情境中，“以牙还牙”（TFT）策略是指首次选择合作，而后每次都复制对手先前使用的策略。假设在一个全部为总是选择背叛的个体的有限群体中进行随机成对互动，作为一种突变策略引入的TFT能够通过选择而被青睐并达到固定状态。我们在离散时间的一般繁殖方案框架下，推导了在弱选择情况下出现这种情况的条件。事实上，我们展示了合作进化的三分之一规则何时以及为何成立，以及它如何扩展为一个更通用的规则。当个体从上一个时间步到下一个时间步留下的后代数量可能有很大差异时，该条件会变得更加严格。这表明在家庭规模分布高度不均衡的群体中，合作的进化会更加困难。文中通过两个例子对此进行了说明。
