Existence of Generalized Game Nash Equilibrium in the Form of Vector Valued Set-valued

The strategy set and payoff function in the common game model are abstracted,and generalized game model of vector-valued set-valued form is constructed,then best response mapping of relevant Nash equilibrium point and generalized game of vector valued set-valued is defined. It is proved that the fixed point of best response mapping and Nash equilibrium point is equivalent. finally,two existence theories of Nash equilibrium point of generalized game model are obtained by doing relevant hypothsis of abstract strategy set and payoff function,and the existence result of Nash equilibrium point is extended.