Game Theory 2-2-12

Game Theory 2-2-12 - GameTheory 2212...

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Game Theory 2-2-12 Is there a dominated strategy? No o Would player 1, play D? Well, he would choose either U or M as strongest strategy but  doesn’t mean he won’t play D. Why? Best Response w/ known probability  o Eu(X, [Pz, (1-Pz]) = Pz * U (x, l) + (1-pz) * U(x, r) o Take expected value EU (U, [½ = L, ½ = R])= ½ (5) + ½ (0)=2.5 EU (M, [½ = L, ½ = R])= ½ (1) + ½ (4) = 2.5 EU (D, [½ = L, ½ = R])= ½ (4) + ½ (2) = 3 Best Response w/ unknown probability  o Unknown probability of player 2 going right EU (U, p{r})= (1-p)(5) + (p)(0) EU (M, p{r})= (1-p)(1) + (p)(4) EU (D, p{r})= (1-p)(4) + (p)(2) L R U 5, 1 0, 2 M 1, 3 4, 1 D 4, 2 2, 3
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o How to get intercepts EU (U, p{r})= (1-p)(5) + (p)(0) Plug in a probability of 0 for player 2 to play right, =5 Plug in a probability of 1 for player to play right, =0 o
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This document was uploaded on 02/19/2012.

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Game Theory 2-2-12 - GameTheory 2212...

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