2004_midterm_1 - 14.12 Game Theory Fall 2004 Midterm 1...

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14.12 Game Theory Fall 2004 Midterm 1 10/13/04 in class (You have 80 minutes. Good Luck!) 1. Consider the following game: A B C a 3,0 0,3 0,x b 0,3 3,0 0,x c x,0 x,0 x,x a. (15pts) Compute two Nash equilibria for x = 1. b. (10pts) For each equilibrium in part a, check if it remains a Nash equilibrium when x = 2. 2. Consider the following game: 1 2,2 2,2 2 X E a b c 1 L R L R 3,1 0,0 0,0 1,3 a. (10pts) Compute two subgame-perfect equilibria. b. (10pts) Represent this game in strategic form. c. (5pts) Find a Nash equilibrium that is not subgame-perfect. 3. Consider two players who own a dollar, which they need to share to consume. Each player cares about his and his opponent’s consumption level. We will first assume that the players are malevolent. The payoff of a player is u = x – α y, where x is his own consumption level, y is his opponent’s consumption level, and α is a number in (0,1). a.
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2004_midterm_1 - 14.12 Game Theory Fall 2004 Midterm 1...

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