Markovian models of three-on-one combat involving a hidden defender

In this paper, Markovian models of three-on-one stochastic firefights between ground-based weapon systems are developed. These models address a common scenario of interest to the military, but one which has been much neglected in analytic combat models, that of combat between a hidden defender and an exposed attacking force. Each combatant must detect an opponent before commencing their firing cycle, a task which is considerably more difficult for the attacker. In the models developed here, the defender detects the exposed attacking group after an exponentially distributed time interval, while each attacker has a fixed probability of detecting the defender via the flash signature produced afer each shot fired by him. This utility of the approach is demonstated by investigating what impact the introduction of a coordinated gun-laying system for the attacking force might have, a system made possible by battlefield digitization. The method used here allows models to be developed incrementally. This and other advances of the Markovian approach are discussed.