Lin Kyle Y. New results on a stochastic duel game with each force consisting of heterogeneous units

Monterey, California: Naval Postgraduate School, 2013. — 25 p.Two forces engage in a duel, with each force initially consisting of several heterogeneous units. Each unit can be assigned to fire at any opposing unit, but the kill rate depends on the assignment. As the duel proceeds, each force -- knowing which units are still alive in real time -- decides dynamically how to assign its fire, to maximize the probability of wiping out the opposing force before getting wiped out. It has been shown in the literature that an optimal pure strategy exists for this two-person zero-sum game, but computing the optimal strategy has remained cumbersome because of the game's huge payoff matrix. This paper gives an efficient algorithm to compute the optimal strategy without enumerating the entire payoff matrix, and offers some insights into the special case, when one force has only one unit.