Some graphical methods for the solution of 3x3 zero-sum games

There are different ways in the literature such as graphic method, linear-programming method, simplex method, Brown-Robinson method related to the solutions of zero-sum games for two people. The graphic methods which are used for the solution of games are important in terms of seeing the results of solution step by step and giving possibility to the using the solution of the game. Graphic methods usually are used according to the size of payoff matrix when it is possible the applicability of the method. For instance, if payoff matrix is from two rows and three columns, the payoff which is acquired by first or second players against each other can be shown in form of affine lines at plane. If the number of row or number of column of payoff matrix is more than two, there isn't any graphic method which is easily understood visually. In this study a graphic method for the solutions of 3 x 3 zero sum games is given. This thesis consists of three sections. At first section, the basic theorem and suggestions which are going to be used for other sections related to game theory at this thesis are given. At the second section, a mathematical method related to 2 x 2 games is given, and also a practical graphical method which can be used at the solutions of 2 x 2 games is suggested. In any case, that payoff matrix is consisted of two lines three columns a method which is used in literature introduced. At third section, it is suggested that a method can be used for the solutions of 3 x 3 games. Firstly, to understand this visual method easily, it is cleared that plane's vertical and horizontal traces and these traces' straight intersection problems are explained. After, beyond this information, the solution of 3 x 3 game is solved by using graphical method.