A robust optimization approach for a two-player force-design game

We present a new approach to force design that relies on robust decision making with a min–max objective, rather than assumptions about the goals and strategy of an opponent. This idea is explored mathematically in the framework of a round-based two-player Stackelberg game representing an arms race, which features the acquisition of assets by both players and an evaluation of the defensive capability against attack from an opponent using a portfolio of possible tactics. Mathematical analysis has been carried out to determine the structure of optimal strategies for this type of game. This allows the strategy of the first player to be represented as a decision tree with possible moves by the second player consisting of convex combinations of extreme points. Using this insight into the structure of solutions, the optimal strategy for the game can be computed using a large linear program. The effectiveness of this approach is demonstrated using numerical examples.