Some Discrete Processes in the Theory of Stochastic Duels

The duel in which the contestant on each side has a fixed kill probability and a random (continuous) time between firings has been previously considered. By limiting the time between rounds to a constant, certain situations in which strong interactions occur are investigated. The models investigated here are (1) the fundamental (one versus one) duel in which firing times are fixed and their ratio is a rational number; (2) the duel with displacements in which two contestants fire simultaneously at fixed intervals and a near miss causes a contestant to displace (and lose a firing turn); (3) multiple duels in which two versus one or two versus two fire simultaneously at fixed intervals; and (4) the cluster duel in which there are several contestants on each side and firing is simultaneous. In the first three, the probability of a given side winning is obtained. In the last, the probability of m contestants on one side killing v of the n contestants on the other side at a single firing is derived.