Symmetric Games

Abstract

In symmetric two-person zero-sum games, both players are guaranteed the existence of a mixed strategy that can prevent a negative expectation. Symmetric games were given particular consideration by Borel. One can restrict attention to symmetric games, since every game can be viewed as part of a symmetric game. The minimax value of a symmetric game is known a priori; it is zero. A typical problem of linear optimization deals with a simple model of a production process and its optimal control. A decision has to be made as to the various quantities in which various products should be produced. There are a number of algorithms for solving linear optimization problems. The most frequently used is George Dantzig’s simplex algorithm. For difficult cases, which arise seldom in practice, there is a better algorithm, discovered in 1984 by Karmarkar. The idea of Dantzig’s simplex algorithm is based on the geometric interpretation of a linear optimization problem.