VALUES OF NOISY DUELS WITH NOT-NECESSARILY EQUAL ACCURACY FUNCTIONS.
Technical summary rept.,
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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Let G sub mnP sub 1, P sub 2 be the noisy duel in which the first player has m bullets with accuracy function P sub 1 and the second player has n bullets with accuracy function P sub 2 where m, n, P sub 1, and P sub 2 are known to both players. Results are well known for the duels in which P sub 1 P sub 2 or when m n 1. The following theorem is proved If P sub 1 and P sub 2 are non-decreasing and continuous on 0, 1 with P sub 10 P sub 20 0 and P sub 11 P sub 21 1, then the game G sub mnP sub 1, P sub 2 has a value. We discuss the structure of epsilon-good strategies and introduce the concept of a good first-shot time. It is shown that although good strategies may not exist, at least one of the players always has a good first-shot time. Author
- Operations Research