Solution Methods for Matrix Games
E.N. Barron · Game Theory · 2013
Graphical methods reveal a lot about exactly how a player reasons her way to a solution. This chapter considers some special types of games for which we actually have a formula giving the value and the mixed strategy saddle points. It starts with the easiest possible class of games that can always be solved explicitly and without using a graphical method. Then, the chapter deals with the case that the game matrix is invertible, or can be made invertible by adding a constant. A related class of games that are also easy to solve is the class of completely mixed games. The chapter also describes symmetric games, and shows how to formulate any matrix game as a linear program. The primal and the dual are needed to find the optimal strategies for each player. Finally, the chapter presents the simplex method specialized for solving matrix games. Controlled Vocabulary Terms game theory; graph; linear programming; payoff matrix