An attack-defense game with matrix strategies

This paper presents the results and the method of analysis for an attack-defense game involving allocation of resources. Each player is assumed to have several different types of resources to be divided in optimal fashion among a fixed set of targets. The payoff function of the game is convex. The “No Soft-Spot” principle of M. Dresher, and the concept of the generalized inverse of a matrix are used to determine optimal strategies for each player and the value of the game.