抽象凸空间中集值映射的不动点定理及其应用

A Fixed Point Theorem for Set-Valued Mapping in Abstract Convex Space with Application

中文关键词:  集值映射  不动点  连续选择  Nash平衡.

英文关键词:set-valued mapping  fixed point  continuous selection  Nash equilibrium.

中文摘要:

      在抽象凸空间中建立了上半连续集值映射的图象逼近连续选择定理、不动点定理. 作为应用,由此证明了抽象凸空间中n人非合作广义博弈Nash平衡的存在性.

英文摘要:

      A new fixed point theorem and the selection property for upper semi-continuous set-valued mappings in abstract convexity space are established. As their applications the existence of Nash equilibrium for $n$-person non-cooperative generalized games is proved.