Combat Control Performance

In Phase I, Metron developed a mathematical approach to tactical decision making based on Bayesian inference and control theory. This theory was demonstrated on three, related one-on-one, submarine engagement problems. The tactics developed in Phase Iare one-sided. The target does not react to the presence or tactics of the friendly ship. The goal of the Phase II work is to extend the Phase I work to account for and anticipate smart behavior by the target. We propose to do this by extending thetactical decision making theory developed in Phase I to a two-sided game in which both platforms can be formulated as a two-sided, non-zero sum game. These games have no minimax solution. Instead, Nash showed that every finite multi-person, general sumgame has at least one equilibrium outcome in mixed strategies. A set of pure or mixed strategies, one for each player, is said to be in equilibrium if no one player can change his strategy unilaterally and gain a higher payoff. We propose to usenon-linear methods, such as path following and one-sided iteration, to find solutions that satisfy (approximately) the Nash equilibrium.