Solution of a Game-Theoretical Model of Resource Allocation

Abstract

We consider a game-theoretical model of defense in which the opponents use several types of infinitelydivisible attack and defense weapons. The defender (first player) payoff is the probability of destroying each attack weapon by at least one of the defense weapons. It is assumed that defense deploys at least one unit of each type of weapons. The optimal defense strategy is a pure maximin strategy, and the optimal mixed attack strategy involves choosing only one of the available attack weapons with certain probabilities. The search for optimal player strategies is reduced to the solution of linear programs.