Silent-noisy marksmanship contest with random termination

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 timeT with cdfH(t). The model is a silent-noisy version of our previous paper (Ref. 8), 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.The author thanks Professor M. Sakaguchi, Osaka University, who contributed to the research on mathematical decision-making problems and expresses appreciation for his continuous encouragement and guidance. The author also thanks Professor G. Kimeldorf, The University of Texas at Dallas, who invited the author to his university. Finally, the author expresses appreciation to Professors K. Sugahara and W. Fukui, Himeji Institute of Technology, for their encouragement and support.