The Method And Improvement For Computing The Solutiongs Of Non-Cooperative Games

In game theory,it is well known that it is very difficult to compute the solutions of the non-cooperative game, especially bimatrix game. Although some common used methods such as Lemke-Howson algorithm can solve some simple bimatrix game theory problems, the process is very complicated, especially when the order of the matrix is very big, the solving process by manual labor is impossible. So we want to solve the matrix game problem by computer. Though some authors gave the methods to computing bimatrix game by employing mathmatica and lingo software packages, the specific algorithm wasn't presented, only using one function of the two software packages to solve an optimize problem.This paper gives some improvement based on the usual algorithms. By employing matlab program, the solution becomes fast and convenient.This paper is organized as follows. In the first section, we introduce the development histories, definition, essential factor of classical games theory and the non-cooperative game, and the background and practical value of the paper. In the second part, we introduce the Two-Person finite game, including fundamental view and the relation of matrix game and the linear programming. Based on some methods in common use, we discuss about a new solution for finite two-person zero-sum game-the avoiding big disadvantage method, and check the result by an example. In chapter III, we introduce the two-person infinite game, including the fundamental rules of arithmetic of countable game, continuous game, game of timing,concave and convex continuous game, fundamental theorem of the existence. And we give some simple methods of the special decision problem. The last chapter introduce Non-cooperative N-person game,including fundamental conception, the existence of Nash equilibrium point, the relation of matrix game and the nonlinear programming. In the end of this chapter, we give some methods to solve the bimatrix game. And based on some existing results, we get the method to solve the bimatrix game problem by using matlab program.