Values and Shooting Times in Noisy Duels
Martin Fox, George Kimeldorf · Journal of the American Statistical Association · 1970
A noisy duel is a zero-sum, two-person game with the following structure. Each player has bullets which he can fire at any time in [0, 1]. If Player i fires at time t, he hits with probability Pi (t). The functions Pi are continuous and nondecreasing with Pi (0)=0 and Pi (1)=1. The number of bullets each player possesses at any time and the functions Pi are known to both. The payoff is 1 to the sole survivor, otherwise 0. This article states the authors' earlier result on the existence of a value of a noisy duel and presents a detailed discussion of the structure of ←-good strategies and criteria for the existence of good first-shot times. We present tables of values and shooting times for noisy duels, which, in some cases, can be used to trace the play of the game. An additional table illustrates how large an arsenal is necessary to overcome the effects of an opponent's superior accuracy.