Section 13 Notes - Killer(Shubik Ch 3 6 There are 3 players...

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Killer (Shubik, Ch 3, 6): There are 3 players A, B, C, each with a balloon and a gun. At each round, one of the players whose balloon is still alive is chosen, with equal probability. That player chooses a balloon that is still alive to aim at, fires, and hits it with a certain probability. When only one balloon is alive, the corresponding player wins $27. Let a,b,c denote the probabilities for A, B, C, respectively. Assume a= 0.8, b=0.6, c =0.4
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No communication between players: Suppose C has been eliminated. P A, B : prob that A wins when pitted against B alone
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No communication between players: Suppose C has been eliminated. P A, B : prob that A wins when pitted against B alone 1/2 1/2 a 1-a b 1-b 1 0 Pab Pab
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No communication between players: Suppose C has been eliminated. P A, B : prob that A wins when pitted against B alone P A,B = (1/2)*a + (1 – a/2 – b/2)P A,B P A,B = a/(a+b) 1/2 1/2 a 1-a b 1-b 1 0 Pab Pab
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No communication between players: Suppose C has been eliminated.
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