G-凸空间中具有G_θ-优化映象的广义博弈的平衡存在定理(英文)

Existence Theorems of Equilibria for Generalized Games with G_θ-majorized Mappings in G-convex Spaces

给出了不具有开原象的Gθ-对应和Gθ-优化映象的概念;在非仿紧的G-凸空间中证明了关于Gθ-对应和Gθ-优化映象的极大元存在定理．作为应用,在非仿紧的G-凸空间中建立了具有无限个选手和Gθ-优化选择对应的定性博弈和广义博弈的平衡存在定理．

New classes of Gθ correspondences and Gθ -majorized mappings without open lower sections are introduced in G-convex spaces. Some existence theorems of maximal elements for Gθ -correspondences and Gθ -majorized mappings are obtained under nonparacompact setting of G-convex spaces. As applications, some new equilibrium existence theorems for qualitative games and generalized games with infinite set of players and Gθ majorized preference correspondences are established under nonparacompact setting of G-convex spaces.