Dual Matrix Game Classification Nash Equilibrium Exists,

This thesis mainly aims to study classification of 2-person non- cooperation finite games,we also investigate generic continuity of functions.The main results is to obtain the essential types of bimatrix games and generic continuity of semicontinuous functions.In Chapter 1,we get the essential types of bimatrix games,according to which, we classify bimatrix games.And we investigate the numbers of pure strategy Nash equilibria for each type of games.In Chapter 2,we study the existence of pure strategy Nash equilibria. Specifically,we generalize the existence of pure strategy Nash equilibria of 2-person zero-sum finite game by Radzik T to 2-person non-zero-sum finite games,give some sufficient conditions for the existence of pure Nash equilibria of bimatrix games.In Chapter 3,we translate lower(upper) semicontinuous bounded above(below) real-valued function f defined on metric space X into set-valued mapping F. From the Aubin theorem,it is easy to prove F is generic continuous on X,then the generic continuity of f on X can be derived.In the end,we give a direct proof of the generic continuity of semicontinuous real-valued function defined on topological space.