GF-空间上Nash平衡的存在性结果

Result of Nash equilibrium existence in GF-space

在抽象凸空间中,给出GF-空间和强Fan-Browder不动点性质的定义,并且在GF-空间中,应用抽象函数代替实值函数作为博弈支付函数,构造GF-空间中博弈模型,应用强Fan-Browder不动点性质证明GF-空间上博弈模型Nash均衡点的存在性.同时也证明了在度量空间和紧拓扑空间上的闭值KKM映射具有有限交性质.

In the abstract convex space, the definitions of GF - space and property of strong Fan-Browder fixed point are given. And in GF - space, real value function is used, instead of abstract function, as game pay function to construct game model in GF space. The property of Strong Fan-Browder fixed point is used to prove the existence of Nash Equilibrium Point of game model in GF-Space and the property of finite commutation of the closed KKM mapping is proved in metric space and compact space.