A Generalized Lagrange-Multiplier Method for Constrained Matrix Games

This paper presents a general method for solving constrained matrix games of a type occurring frequently in military and industrial operations research. The usual context is the optimal allocation of constrained resources by two opposing sides among a series of independent cells such that the payoff overall is the sum of the payoffs at each cell. The cells themselves might represent separate invasion or supply routes, battlefields, individual targets, or marketing ventures. Generalized Lagrange multipliers (Everett multipliers) are used to effect the solution. It is shown that the basic properties of the games preclude the possibilities of nonconcavities or extraneous solutions.