The Existence Of The Solution And Evolutionary Stability For Multiobjective Game

This paper proved the existence of solutions for multibjective generalized game by the results we get for vector quasi-equilibrium problems. Then we proposed a notion of multiobjective weighed evolutionary stability strategy, and induced some evolutionary stability results about multiobjective weighed evolutionary stability strategy. These results are new and independent of the literature reference.First of all, background of related problems about vector quasi-equilibrium problems such as: vector equilibrium problems, vector variational inequation problems, vector complementary problems, vector saddle point problems vector optimal problems, and evolutionary game theory be introduced, which is the basis of viewpoint of this paper.Third section is the existence of solution for vector quasi-equilibrium with its applications. The property of vector valued function' s quasi-concave(convex) and well known Browder fixed point theorem become our great assistant for proof of the existence of solutions for vector quasi-equilibrium, in addition, in baire space, stability of solutions for vector quasi-equilibrium be studied, and the existence and stability of weak Pareto-Nash equilibrium point about multiobjective generalized game follows.Fourth section proposes a new notion named multiobjective weighed evolutionary (weak) stability strategy from analysis of necessity of research...