TABLES OF VALUES AND SHOOTING TIMES IN NOISY DUELS.
Martin Fox, George Kimeldorf · 1968
Abstract : A noisy duel is a zero-sum, two-person game with the following structure: Each player has bullets which he can fire at any times in (0, 1). If Player i fires at time t, he hits with probability P sub i(t). The functions P sub i are continuous and nondecreasing with P sub i(0) = 0 and P sub i(1) = 1. The number of bullets each player possesses at any time and the functions P sub i are known to both. The payoff is 1 to the sole survivor, otherwise 0. This paper reviews the authors' earlier work on the existence of values and the structure of epsilon-good strategies. Tables of values and shooting times for noisy duels are presented, 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. (Author)