1,1 | 2,2 | 3.4 | 9,3 |
2,5 | 3,3 | 1,2 | 7,1 |
Find all pure-strategy equilibria of the game.
Now find a mixed-strategy equilibrium of the game. What are the players’
expected payoffs in this equilibrium?
1,1 2,2 3.4 9,3 2,5 3,3 1,2 7,1 Find all pure-strategy equilibria of the game. Now...
Find all mixed strategy Nash Equilibria of the following game: X Y Z A 2,2 4,0 1,3 B 1,3 6,0 1,0 C 3,1 3,3 2,2
3. Consider the following two-player game in strategic form LM R A 2,2 2,2 2,2 В 3,3 0,2 0,0 С 0,0 3,2 0,3 This game will demonstrate several methods for ruling out possible mixed- strategy equilibria (a) What are the pure strategy equilibria? (b) Show that there does not exist an equilibrium in which Player 1 (the row player) assigns strictly positive probability to A, to B, and to C. (c) Show that there does not exist an equilibrium in...
#2. Find all pure and mixed strategy Nash equilibria (if any) in the following game. U 1,1 0,0 0, -1 S 0,0 1,1 0, -1 D.0.0 0,-1
a.) Find all pure-strategy Nash equilibria. b.) *Find all mixed-strategy Nash equilibria. c.) Explain why, in any mixed-strategy equilibrium, each player must be indifferent between the pure strategies that she randomizes over. Consider the following game: - 2 LR 2
Find all of the pure and mixed strategy Nash equilibrium of the following game: Left 5,10 3.7 2,5 Top 1 Middle Bottom 2 Center Right 4,4 8.8 6.5 2,7 2,2 2,1 Figure 1: A Random Game
Find all pure strategy Nash Equilibria in the following games a.) Player 2 b1 b2 b3 a1 1,3 2,2 1,2 a2 2,3 2,3 2,1 a3 1,1 1,2 3,2 a4 1,2 3,1 2,3 Player 1 b.) Player 2 A B C D A 1,3 3,1 0,2 1,1 B 1,2 1,2 2,3 1,1 C 3,2 2,1 1,3 0,3 D 2,0 3,0 1,1 2,2 Player 1 c.) Player 2 S B S 3,2 1,1 B 0,0 2,3
Determine ALL of the Nash equilibria (pure-strategy and mixed-strategy equilibria) of the following 3 games: Player 1 H T Player 2 HT (1, -1) (-1,1) | (-1,1) (1, -1) | Н Player 1 H D Player 2 D (2, 2) (3,1) | (3,1) |(2,2) | Player 2 A (2, 2) (0,0) Player 1 A B B (0,0) | (3,4)
Consider the following extensive-form game with two players, 1 and 2. a). Find the pure-strategy Nash equilibria of the game. [8 Marks] b). Find the pure-strategy subgame-perfect equilibria of the game. [6 Marks] c). Derive the mixed strategy Nash equilibrium of the subgame. If players play this mixed Nash equilibrium in the subgame, would 1 player In or Out at the initial mode? [6 Marks] [Hint: Write down the normal-form of the subgame and derive the mixed Nash equilibrium of...
For each tree, find all pure strategy Nash equilibria (NE), and all pure strategy subgame-perfect Nash equilibria (SPNE). In every tree, payoffs are in alphabetical order. You can gain up to 10 points per tree (5 points for NE, 5 points for SPNE). Ann Ann Bob Bob Bob 2 2.2 1,0 2.2 2,0 Tree 1 Tree 2 Ann Ann Bob Bob 1,1 1,1 1,1 10 o,I 1,0 Tree 3 Tree 4
Some Game Theory Problems 3. Find all of the pure strategy Nash Equilibria of the following simultaneous move game. After solving it as a simultaneous move game, write it as a sequential move game with column moving first. Drow the game tree and solve for the Subgame Perfect Nash Equilibrium. Column 9,4 1,10 15,7 15,5 14,8 3,10 12,18 20,12 Row C 7,8 6,8 20,10 3,3 15,9 15,0 14,2 9,1 20,18 2,9 10,14 19,20