[SUBMARINE, Anti-, Warfare] Balinski, Michel, et al. Final Report. A Study of Optimal Patrol and Transit Strategies in a Rectangular Barrier Zone Using Mathematical Games. Written and produced by Mathematica, prepared for the Office of Naval Research, 1967. 77pp.

• "The strategies available to a patrol sub seeking to maximize the probability of detecting a transistor in a rectangular zone are analyzed..." (Keywords identified: Bowtie Patrols, Matrix Games, Stationary Patrols, Optimal Straight Line transits.) WorldCat OCLC locates only one copy. $150 "Three classes of models are treated (1) fixed shape patrol patterns (e.g., Bow Tie with crossover angle to be optimized), (2) linear patrols with delays at a finite number of stations, optimization being over the delay time distribution, and (3) linear patrols with optimization over speed. In all the games analyzed, transitor strategies were also optimal for a suitably restricted class of transit lanes and speeds. The problem of securing first detection is considered where appropriate. The payoff function for most of the games is probability of detecting the transitor during the time interval necessary for a complete transit through the zone. Fixed radius of detection is assumed in the first two classes of model; dependence on speeds of both subs is assumed in the third. All three sets of assumptions point to the strategic merit lf linear patrols which have at least two widely differing speeds: in geometric terms the patrol pattern should be a sequence of localized delay patterns joined by high-speed straight-line segments."-_WorldCat Identities.