Berge极大值逆定理与Nash平衡定理  

An Inverse of Berge Maximum Theorem and Nash Equilibrium Theorem

作　　者：丘小玲 贾文生 QIU XIAOLING, JIA WENSHENG(School of Mathematics and Statistics, Guizhou University, Guiyang 550025, Chin)

机构地区：[1]贵州大学数学与统计学院

出　　处：《应用数学学报》2018年第2期280-288,共9页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(No.11561013,71461003,11661019);人社部留学归国人员择优项目(No.2015192);贵州省科技厅联合基金(黔科合LH字[2014]7643,[2016]7425);贵州大学引进人才基金(No.201405)资助

摘　　要：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.

关 键 词：Berge极大值逆定理 Nash平衡定理 拟变分不等式 Von Neumann引理 Gale- Nikaido—Debreu引理的推广定理 伪连续 

分 类 号：O177[理学—数学]