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- Problem 1. Consider the following strategic game: A В с D C 10,10 6,8 4,5 10,1 y 7,4 62,10 4,5 10,3 8,6 8,6 8,5 10,4 a) Find all pure strategies dominated by a pure strategy. b) Find all pure strategies dominated by a mixed strategy. c) Find all pure NE. d) Find all mixed NE.Problem 1. Consider the following strategic game: A В D 10,10 6,8 4,5 10,1 y 7,4 62,10 4,5 10,3 8,6 8,6 8,5 10,4 a) Find all pure strategies dominated by a pure strategy. b) Find all pure strategies dominated by a mixed strategy. c) Find all pure NE. d) Find all mixed NE.3) Consider the following two extensive form games and answer the following questions. How many subgames present in the following games? Find all pure strategies SPNE. Find all pure strategies NE of these games. Game A Game B u (5,3) u (0,2) 2 2 L L (-5,4) d (0,0) 1 1 1 (1,-5) (-10,-10) u R (2,3) A M 2 R 2 r d 1 (8,1) B (2,0) (2,2)
- 2. Find all pure and mixed strategy Nash equilibria of the following game. X Y Z X 4,2 0,0 0,1 0,0 2,4 1,3 Y16) Convert the following extensive form game into a normal form game. Solve the game to find all pure strategy Nash equilibria. 1 A B 2 W X Y 3, 3 1, 2 2, 1 4, 4game. Find all the pure strategy and mixed strategy Nash equilibria in the following Player 1 A B C Player 2 M R 4,1 1,0 3,2 0,1 2,0 2,2
- 3. Nash Equilibria Consider the following (normal-form) game. Compute a Nash Equilibrium of this game. U C D L | M R 5,0 1,3 4,0 2,4 1,4 3,5 0,1 1,0 5,017) Convert the following extensive form game into a normal form game. Solve the game to find all pure strategy Nash equilibria. 1 A 2 2 W X W 4,3 1, 2 2, 4 3, 1Q2 Consider the following game. (a) Find all pure-strategy Nash equilibria. (b) Find all mixed-strategy Nash equilibria. 2, 4 6, 0 5,1 1,9 A В
- 2. Consider the following game: u 1 r 6,0 0,6 d 3,2 6,0 Are there any Nash equilibria in pure strategies for this game? Find the mixed strategy Nash equilibrium.3. 1 2 J K 2 1 2 0 0 K 3 3 E/ 1.1 2.2 B G 2 -2 a.) How many Subgames does this Game have? b.) Convert this Game Tree into matrix form. c.) Find all Pure Strategy Nash Equilibria of this Game. d.) Find all Subgame Perfect Nash Equilibria of this Game. (Pure and Mixed) 2 2.216. Consider a game with two players, each with three strategies. Given the payoff matrix shown below, determine which pair of strategies is a Nash equilibrium. Player One X Y 1 3. X' 3 1 4 Player Two Y 5 0. 3 Z' 4 (a) X, X' 21 1.