In this paper, we perform an analysis of the fighter bomber duel where player one (the fighter) has a discrete resource, as in a single shot which he can fire at any point, and the other player (the bomber) has a continuous resource (machine gun), which she can distribute as a function of time. We look at this problem applied towards the safety of an autonomous system in a competitive environment. The specific problem we address is probability of failure, can we put a bound on the probability that an autonomous system completes its objective in a hostile environment?
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