Linear Programming and Two-Person Zero-Sum Games

The equivalence between linear programming (LP) and two-person zero-sum games (also commonly referred to as matrix games) was established when the minimax theorem in game theory proved to be equivalent to the duality concept in LP. The equivalence is discussed as follows: Given a general matrix game, the associated primal-dual LP problems will be formulated, and, conversely, given an LP problem with a minimization objective function, a skew-symmetric payoff matrix of the equivalent symmetric game will be constructed. In either case, once the solutions to the equivalent problem are found, it is a simple task to retrieve the solutions to the original problem. Examples are provided to illustrate the transformation procedures, and different types of constraints for the given LP problem are also considered (normal, standard and mixed).