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The marksmanship contest game with random termination is a fundamental two-person game of timing under an uncertain environment. In this paper, we formulate a unied marksmanship contest game with random termination and show that it can be further classied intove different games. We derive the optimal solutions of these games of timing, which are categorized into the Nash equilibrium strategy and the Stackelberg strategy. Our results involve the well-known results by Teraoka (1983) and Baston and Garnaev (1995) as special cases and at the same time give new insights for different types of game.

STOCHASTIC MARKSMANSHIP CONTEST GAMES WITH RANDOM TERMINATION — SURVEY AND APPLICATIONS