Accession Number : AD0668389
Title : VALUES OF NOISY DUELS WITH NOT-NECESSARILY EQUAL ACCURACY FUNCTIONS.
Descriptive Note : Technical summary rept.,
Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
Personal Author(s) : Fox,Martin ; Kimeldorf,George S.
Report Date : JAN 1968
Pagination or Media Count : 20
Abstract : Let G sub mn(P 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 1(0) = P sub 2(0) = 0 and P sub 1(1) = P sub 2(1) = 1, then the game G sub mn(P 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)
Descriptors : (*GAME THEORY, PROBLEM SOLVING), PROBABILITY, SET THEORY, DECISION THEORY, NUMERICAL METHODS AND PROCEDURES, THEOREMS
Subject Categories : Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE