Mixed-Strategy Solutions to Integer Prim-Read Defense Problems
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The integer Prim-Read deployment and firing schedule problem for a point defense was solved by Burr, Falk, and Karr in 1985. This paper investigates the consequences if the offense cannot acquire reliable knowledge of the firing schedules of the defense. The problem is readily formulated as a two-person zero-sum game in normal form in which the payoff is the average return. The paper also establishes a relationship between this average return game and the "constrained offense game" in which the offense and defense attempt to maximize and minimize total damage, subject to an explicit upper limit on the attack size against a set of many identical targets. This result extends to other closely related problems. Examples are given of other offense-defense situations for which a game-theoretic approach is called for even if other approximate approaches must be used in practice.
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