soln8 - Econ 354K Game Theory Solutions to Problem Set No....

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1 Econ 354K Game Theory Solutions to Problem Set No. 8 1. Dutta 5.2 Pure strategy Nash equilibria: all cells with a payoff of (1,2). Each player believing that the other is equally likely to choose any of the available strategies is a mixed-strategy NE. T\B 1,2 1,3 1,4 2,3 2,4 3,4 1 0,1 0,1 0,1 1,2 1,2 1,2 2 0,1 1,2 1,2 0,1 0,1 1,2 3 1,2 0,1 1,2 0,1 1,2 0,1 4 1,2 1,2 0,1 1,2 0,1 0,1 2. Dutta 5.4: br(0) = {0,1}; br(j>0) = 0. 3. Dutta 5.5: NE = {00, 01, 10} For questions 5.4 and 5.5, you could also fill in a payoff matrix using using x yx +− for player 1 and x yy + for player 2 with { } , 0,1,2,3,4 xy to determine the best responses and the Nash equilibria 1\2 0 1 2 3 4 0 0.0 , 0.0 1.0 , 0.0 1.4 , -0.6 1.7 , -1.3 2.0 , -2.0 1 0.0 , 1.0 0.4, 0.4 0.7, -0.3 1.0, -1.0 1.2, -1.8 2 -0.6, 1.4 -0.3, 0.7 0.0, 0.0 0.2, -0.8 0.4, -1.6 3 -1.3, 1.7 -1.0, 1.0 -0.8, 0.2 -0.6, -0.6 -0.4, -1.4 4 -2.0, 2.0 -1.8, 1.2 -1.6, 0.4 -1.4, -0.4 -1.2, -1.2 4. Three-player game: (ABC, CBS, NBC) Eliminate strictly dominated strategies first. NBC: live CBS Live taped live .42,.34,.24 .37,.40,.23 ABC taped .40 ,.34,.26 .34, .26,.40 NBC: taped CBS Live taped live .34,.26,.40 .60,.22,.18 ABC taped .24 ,.60,.16 .42, .34,.24 So, ABC eliminates “taped”.
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2 The game becomes,
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soln8 - Econ 354K Game Theory Solutions to Problem Set No....

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