Genetic Differentiation Algorithm And Many Person Noncooperative Game's Nash Equilibrium

In game theory, people study decisions for environments where various players interact to get best payoff. Although Nash had proved that any finity game has mixed equilibrium in 1950, he didn't give an universal solution to Nash equilibrium at last.At present, though we have some methods to solve Nash equilibrium, they aim at those subjects that comfined under some conditions, and hence those resolvents have some limitations. For example, geometrical figure method aims at (only fit) low order matric game, while the order exceed three, it is hard to use this intuitionistic method. For an other example, Lemke-Howson algorithm bases on the thought of linear programming which is used on matric game; so it will be quite hard when this algorithm is used to handle issues with nonlinear conditions. There are other thought which lay on gradient descent idea to strengthen the payoff function condition, they also have similar problems. However, practical problems, especially military affairs games, corresponding payoff functions commonly haven't the characters necessary to the above algorithms. This limitation comfines the applying ranges of many game theoretical methods including Nash equilibrium.Essentially, in game theory, people gain optimal and assured solutions under some uncertainty conditions as soon as possibe, while soft computation or int(?)lligence computation is a sort of effective method to solve uncertainty problems; so it is a natural idea to solve Nash equilibrium problem with soft computation. Hense, we consider using genetic algorithm who have the character of survival of the fittest. But when we use simple genetic algorithm to solve Nash equilibrium, we find this algorithm has premature convergence phenomenon, so it can not sovle Nash equilibrium who is a mutiple hump problem.In this paper, we use genetic differentiation algorithm to get the Nash equilibrium in many person noncooperative game. And experiments show this new algorithm get better results in solving Nash equilibrium than simple genetic algorithm.