Berge极大值逆定理与Nash平衡定理

An Inverse of Berge Maximum Theorem and Nash Equilibrium Theorem

本文运用Berge极大值逆定理和Nash平衡定理，通过构造适当的支付函数，直接推导出了拟变分不等式、广义变分不等式、VonNeumann引理，以及Gale—Nikaido—Debreu引理的推广定理．同时也提供了一个将上半连续凸紧值的集值映射问题转化为一个二元函数来处理的方法．这些结果和证明方法都是新的．

By constructing an appropriate payoff function, quasi-variational inequality, generalized variational inequality, Von Neumann Lemma and the extension of Gale-Nikaido- Debreu Lemma, can be derived from Nash equilibrium theorem, with the aid of the inverse of the Berge maximum theorem. Moreover, all important method is provided that an upper semicontinuous and convex compact set-valued mapping problem is converted into a binary function. Our results and proofs are all new.