对Eric van Damme引理的再探讨

Re-discussion on Eric van Damme Lemma

双矩阵博弈中的一个著名定理——完美均衡等价于非劣纳什均衡的证明依赖于van Damme给出的一个引理.有研究者认为,Damme引理的充分条件并不成立,其结果将导致定理有可能不成立.经过认真研究,得出的结论是,认为Damme引理不成立的理由并不充分,而是忽略掉了一个重要条件导致的结果,并对此进行了说明,并给出了Damme引理的一个严格证明.

A non-inferior Nash famous theorem in bimatrix game is that the proof for that perfect equilibrium is equivalent to Equilibrium depends on a lemma given by van Damme. Some researchers believe that the sufficient and necessary condition for Damme Lemma is untenable, whose consequence will lead to the falseness of Damme Lemma. After careful study on this, the conclusion is that the reason for the falseness of Damme Lemma is not sufficient, but the result caused by an important condition is neglected, this paper explains this and gives a strict proof for Damme Lemma.