楼主所说的不是均衡。只要是有限次。博弈参与者都完全理性的知道的话。

那么在最后一期必然会出现背叛。也就是说，所谓的以牙还牙策略在最后一期是不存在的。

既然你在最后一期是无法以牙还牙的，那么之前怎么可能以牙还牙呢？

lz可以写出你思路的全过程，比如得益函数，等等等等。

逆推的思路是这样的。毫无疑问，最后一期一定是背叛。不存在所谓以牙还牙。

那么倒数第二期博弈双方的得益函数也是可以写出的。当期收益加下期收益的折现。

由于下期收益固定。当期博弈与单次博弈相同，故背叛。以此类推。

楼主的推理已经超出模型的假定了。

说的对！

alexruby 我觉得你挺专业的~··~

[此贴子已经被作者于2009-5-25 23:42:00编辑过]

这一点在经济学课堂上的随机实战模拟可以得出类似的结论。

市场模拟可以得出类似的结论，当不知道对方是否背叛的情况下总是先背叛。

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" Tit for Tat" strategy is not really that good. The aurthor who suggested it actually cheated in his paper. You can find it in the book "Game Theory-Very Short Introduction". There is anther possibility that one player made a mistake or did not know how to play, then you get problem. Some suggest that "Two Tit for a Tat". However, it is still arguable. One player could pretend that he does not know the rule and play Cheat until his opponent almost gives up the hope to play Cooperate, then he starts to play Cooperate. As we can see, there is no good way to solve Prisoners' Dilemma. You also should read Schelling's paper "Hockey Helmets, Concealed Weapons, and Daylight Saving: A Study of Binary Choices with Externalities". He suggests that we should not try to solve Prisoners' Dilemma in some situation in which some people cooperate and others do not cooperate is the social optimal, which is better than everyone cooperates. The problem is who should cooperate.

In reality, nobody thinks about the long run because "After all, in the long run we are dead."

只要信息是完全的，有限重复囚徒困境博弈中，（不坦白、不坦白）一定不是均衡策略。楼主的论断是错误的，无论采用怎样的策略，都不能使得这一策略成为均衡策略。alexruby 的解释完全正确。

在有限次囚徒困境，如果期望上述策略成为均衡策略。必须绕开完全信息限制。关于这一点，KWMR他们在80年代进行的声誉理论等研究，都基于此。