A Helicopter Versus Submarine Search Game

Abstract

How should helicopters use their dipping sonar so as to search for a submarine now submerged and attempting to escape, which had been sighted a short time before? By some approximations to reality and a shift in the point of view the problem is brought to a simple two-person zero-sum game in which one side juggles areas and the other probability distributions. The solutions are exhibited and proved to be solutions by direct application of the definition of optimal strategies for a game. The solution may be understood with very little mathematical knowledge. It turns out that the helicopters should, generally speaking, spiral inward in the relative speed circle.