The Stability Of The Sets Of Nash Equilibrium Points Of Infinite Games

In this thesis, we focus on discussing the stability of solutions of non-cooperative games with infinitely many pure strategies, including the generic stability of solutions of infinitely many pure strategies and the existence of the essential components of the sets of Nash equilibrium points of infinite games.This thesis is organized as follows:Chapter 1 We recall some notions and results used in our analysis in this thesis, including topology on closed subset spaces, measure integral on compact metric spaces, continuity of set-valued mappings on topology spaces.Chapter 2 We definite a new distance improving upon levy-prohorov distance on all measure set of compact measure space, and we prove the equivalence of the topology and weakly topology which the distance deduce.Chapter 3 We study the stability of the set of mixed Nash equilibrium points of N-person non-cooperative games with compact metric spaces of infinite pure strategies and continuous payoff functions. First, we discuss the generic stability of solutions of infinite pure strategies in the graph topology case, then we obtain the existence of essential components of the perturbations of best reply correspondences which is deduced from the new definited levy-prohorov distance in chapter 2 and the existence of essential components of the sets of fixed point on the mixed strategy profile spaces.