“What accounts for TIT FOR TAT’s robust success is its combination of being nice, retaliatory, forgiving, and clear. Its niceness prevents it from getting into unnecessary trouble. Its retaliation discourages the other side from persisting whenever defection is tried. Its forgiveness helps restore mutual cooperation. And its clarity makes it intelligible to the other player, thereby eliciting long-term cooperation.”

TIT FOR TAT的四点属性,不首先欺骗,有仇必报,报酬后会选择原谅,以及非常容易辨认的策略。其实就是一种阳谋,告诉对方自己的策略,有理智的玩家自然会辨认出长期合作对双方都是最好的选择。

“Just how broadly applicable was the proposition about TIT FOR TAT which said that it was collectively stable if and only if the future of the interaction was sufficiently important? The next proposition says that this result is very general indeed, and actually applies to any strategy which may be the first to cooperate.”

这里指的stable是说,假设所有玩家都使用一个策略,那这个策略是stable当且仅当另一个玩家使用一种其他任何策略加入游戏时,那种策略无法取得等好的成绩。TIT FOR TAT或是任何选择首先合作的策略,都需要未来轮次的重要性足够高,换句话说,会有长期交往的可能性,而不是一锤子买卖。

“The reason is that for a strategy to be collectively stable it must protect itself from invasion by any challenger, including the strategy which always defects. If the native strategy ever cooperates, ALL D will get T on that move. On the other hand, the population average among the natives can be no greater than R per move. So in order for the population average to be no less than the score of the challenging ALL D, the interaction must last long enough for the gain from temptation to be nullified over future moves.”

这里更具体地解释了原因,假设一个入侵策略是全部背叛的话,为了使得第一次背叛的多出来的收益被抵消,那么未来就要有足够多的轮次通过彼此互相合作的收益来弥补。