Silent-noisy marksmanship contest with random termination (Q1061022)

We consider a marksmanship contest in which Player I has one silent bullet, whereas Player II has one noisy bullet, the first contestant to hit his target wins, and the contest is to be terminated at a random time T with cdf H(t). The model is a silent-noisy version of our previous paper [ibid. 40, 379-396 (1983; Zbl 0494.90091)], and an extension of silent-noisy duel to nonzero-sum games of timing under an uncertain environment. It is shown that the uncertainty on the termination of the contest has influence on the equilibrium strategies and the equilibrium values, but the silent player has no advantages over the noisy one, in such a nonzero-sum model.