2005_midterm_1 - 14.12 Game Theory Muhamet Yildiz Fall 2005...

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Unformatted text preview: 14.12 Game Theory Muhamet Yildiz Fall 2005 Midterm 1 October 17th, 2005 (80 minutes) Good Luck! 1. Below there are two pairs of games. For each pair check whether they represent the same preference relation on the lotteries with strategy pro f les as their outcomes. (Show your work.) (a) (10 points) L R T 1,0 4,1 B 2,4 3,2 L R T 1,0 4,1 B 2,3 3,2 (b) (10 points) L R A 0,1 6,4 B 2,4 4,7 C 4,-2 2,1 L R A 1,0 4,1 B 2,1 3,2 C 3,-1 2,0 2. (25 points) Find all the Nash equilibria in the following game. (Dont forget the mixed strategy equilibrium, which is 13 points.) L M R A 1,0 4,1 1,0 B 2,1 3,2 0,1 C 3,-1 2,0 2,2 3. Consider the following game in extensive form. 1 L R 2 a b c 1 l r 2 x y 1 1 2 2-1 4 1 1 1 1 L R 2 a b c 1 l r 2 x y 1 1 2 2-1 4 1 1 1 1 (a) (10 points) Use backwards induction to compute an equilibrium. (b) (10 points) Write this game in normal form. (c) (10 points) Compute the set of rationalizable strategies....
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2005_midterm_1 - 14.12 Game Theory Muhamet Yildiz Fall 2005...

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