Types Of Non-cooperative Games Optimal Solution Algorithm And Its Application

There are some methods to solve the Nash equilibrium, sush as elimination method, streak plate method, arrow point method and Lemke-Howson algorithm. But these methods only give rise to pure strategy Nash equilibrium, as to the mixed strategy Nash equilibrium, there is little they can do about it. Lemke-Howson algorithm give the simplex solution, the classical Lemke-Howson algorithm may not only find the pure strategy Nash equilibrium, but also find the mixed strategy Nash equilibrium. Although it has been revised several times, the use of algorithm for solving the Nash equilibrium of the bimatrix game still has a lot of calculation, and it isn't suitable for calculating the coordination equilibrium.The PSO algorithm establishes evolutionary model of the game from the swarm intelligence perspective, which provides a brand-new kind way to solve Nash equilibrium of the n persons's noncooperative game. The coordination equilibrium and the Nash equilibrium both have multiplicity and complexity of the algorithm. To a certain extent, the method of finding Pareto optimal coordination equilibrated situation solves multiplicity problems. The main contribution of the paper is to put forward the principal diagonal dominant norm for determining coordination equilibrated situation. On the basis of the latest research work of the PSO at home and abroad. By redefining particle in the PSO algorithm and fitness function, we find the coordination equilibrium by programming. Besides, we discuss the relationship among coordination equilibrated situation, Nash equilibrated situation and Pareto optimal situation in coordination mixed strategy, and we look for Pareto optimal situation among the infinite coordination equilibrium by linear programming method.