A necessary and sufficient condition of distinguishing pure strategy Nash equilibrium existence in static games;

A necessary and sufficient condition of pure strategy Nash equilibrium was given in finite static games,and then a distinguishing method for pure strategy Nash equilibrium existence in finite static games was provided.

In the present paper, a max\|min theorem and a max theorem are proved on local convex topological linear spaces, as an application, it is obtained that there exists optimal mixed strategies in a two\|person game with an infinite pure strategy set.

On the basis of intruducing briefly grey system situation decision, this paper applies multiobjective and multistage grey situation decision to the optimal selection of river serial developing schemes, gives a real example and gains a good result.

It involves the grey target decision and situation decision on simple-objective.

Using a practical example, this paper discusses an application of the grey theory and methods in particular the grey situation decision making to enterprise s multiproduct multigoal price regulation.