Player 1 \ Player 2 1 2 3 A 5,9 4,7 3,2 B 2,1 5,3 6,7...
| Player 1 \ Player 2 | 1 | 2 | 3 |
| A | 5,9 | 4,7 | 3,2 |
| B | 2,1 | 5,3 | 6,7 |
| C | 1,7 | 3,8 | 2,9 |
Player 2 believes Player 1 is playing a mixed strategy and may have an idea of the probabilities Player 1 chooses for each strategy. Describe the Player 1 probabilities that would justify each pure strategy for Player 2.
***Please do not copy/paste an incorrect answer. If you don't know how to do it, please do not further confuse me! Thank you
Homework Answers
Q.2 Consider the following normal-form game: Player 2 Player 1 3,2 1,1 -1,3 R. 0,0 Q.2.a...
Q.2 Consider the following normal-form game: Player 2 Player 1 3,2 1,1 -1,3 R. 0,0 Q.2.a Identify the pure-strategy Nash equilibria. Q.2.b Identify the mixed-strategy Nash equilibria Q.2.c Calculate each player's expected equilibrium payoff.
Game Theory Nash Equilibrium Mixed strategies for 2*3 Matrix
a) Eliminate strictly dominated strategies.b) If the game does not have a pure strategy Nash equilibrium,find the mixed strategy Nash equilibrium for the smaller game(after eliminating dominated strategies). Player 2Player 1abcA4,33,22,4B1,35,33,3
Player 2 L R U 2,1 2,0 Player 1 D 1, 2 3, 1 The above...
Player 2 L R U 2,1 2,0 Player 1 D 1, 2 3, 1 The above figure shows the payoff matrix for two players, Player 1 and Player 2. Player 1's payoff is listed first in each cell. A Nash equilibrium of this game is that Player 1 chooses D and Player 2 chooses L. Player 1 chooses D and Player 2 chooses R. Player 1 chooses U and Player 2 chooses L. Player 1 chooses U and Player 2...
Problem 1: Consider the following simultaneous move game with two players, denoted by 1 and 2: 1 2 T B L 1,0 0,2 M R 0,...
Problem 1: Consider the following simultaneous move game with two players, denoted by 1 and 2: 1 2 T B L 1,0 0,2 M R 0,1 5,0 2,1 1,0 1. Is there a strategy for any of the players which a player would never choose? 2. If there is a strategy which a player never chooses (it is called, a dominated strategy), and this fact is known among the players, find the equilibria of the game. Hint: In a mixed...
Please answer 3 Questions, thank you. 4. Consider the following game: PLAYER 2 (0,3) (2,0) (1,7)...
Please answer 3 Questions, thank you.
4. Consider the following game: PLAYER 2 (0,3) (2,0) (1,7) PLAYER 1 (2,4) (0,6) (2,0) (1,3) (2,4) (0,3) a) Does this game have any pure-strategy Nash equilibrium? If so, identify it (or them) and explain why this is an equilibrium. b) Find a mixed-strategy Nash equilibrium to this game and explain your calculations. Note: a mixed strategy for player i may be expressed by o; = (P1, P2, 1- P1 - p2). c) Is...
In the extensive form representation of the game between Player 1 and Player 2, Player 1...
In the extensive form representation of the game between Player 1 and Player 2, Player 1 moves first and chooses L or R. If Player 1 chooses R the game ends, if Player 1 chooses L then Player 1 and 2 play a simultaneous move game. The game has______________ pure strategy Nash equilibria and__________ pure strategy Subgame Perfect Nash Equilibria (SPNE). The maximum payoff Player 2 gets in a SPNE is___________ . (Please, enter only numerical answers like: 1, 2,...
Consider the following extensive-form game with two players, 1 and 2. a). Find the pure-strategy Nash...
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...
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,...
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. (25 pts) Consider a two player game with a payoff matrix (1)/(2) L U D...
2. (25 pts) Consider a two player game with a payoff matrix (1)/(2) L U D R (2,1) (1,0) (0,0) (3,-4) where e E{-1,1} is a parameter known by player 2 only. Player 1 believes that 0 = 1 with probability 1/2 and 0 = -1 with probability 1/2. Everything above is common knowledge. (a) Write down the strategy space of each player. (b) Find the set of pure strategy Bayesian Nash equilibria.
2,4 3, 6 6,7 7, 3 8, 1 9.2 4, 5 5, 4 Consider the extensive...
2,4 3, 6 6,7 7, 3 8, 1 9.2 4, 5 5, 4 Consider the extensive form game above. The game has for Plasyer 2. In the backward induction equilibrium in pure strategies Player 2 gets a payott of subgames. The strategy profile (AGUKM, CED) leads to a payoff of for Player 1 and (Please, enter only numerical values like: 0. 1.2,3)
Q.2 Consider the following normal-form game: Player 2 Player 1 3,2 1,1 -1,3 R. 0,0 Q.2.a Identify the pure-strategy Nash equilibria. Q.2.b Identify the mixed-strategy Nash equilibria Q.2.c Calculate each player's expected equilibrium payoff.
Player 2 L R U 2,1 2,0 Player 1 D 1, 2 3, 1 The above figure shows the payoff matrix for two players, Player 1 and Player 2. Player 1's payoff is listed first in each cell. A Nash equilibrium of this game is that Player 1 chooses D and Player 2 chooses L. Player 1 chooses D and Player 2 chooses R. Player 1 chooses U and Player 2 chooses L. Player 1 chooses U and Player 2...
Problem 1: Consider the following simultaneous move game with two players, denoted by 1 and 2: 1 2 T B L 1,0 0,2 M R 0,1 5,0 2,1 1,0 1. Is there a strategy for any of the players which a player would never choose? 2. If there is a strategy which a player never chooses (it is called, a dominated strategy), and this fact is known among the players, find the equilibria of the game. Hint: In a mixed...
Please answer 3 Questions, thank you.
4. Consider the following game: PLAYER 2 (0,3) (2,0) (1,7) PLAYER 1 (2,4) (0,6) (2,0) (1,3) (2,4) (0,3) a) Does this game have any pure-strategy Nash equilibrium? If so, identify it (or them) and explain why this is an equilibrium. b) Find a mixed-strategy Nash equilibrium to this game and explain your calculations. Note: a mixed strategy for player i may be expressed by o; = (P1, P2, 1- P1 - p2). c) Is...
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...
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. (25 pts) Consider a two player game with a payoff matrix (1)/(2) L U D R (2,1) (1,0) (0,0) (3,-4) where e E{-1,1} is a parameter known by player 2 only. Player 1 believes that 0 = 1 with probability 1/2 and 0 = -1 with probability 1/2. Everything above is common knowledge. (a) Write down the strategy space of each player. (b) Find the set of pure strategy Bayesian Nash equilibria.
2,4 3, 6 6,7 7, 3 8, 1 9.2 4, 5 5, 4 Consider the extensive form game above. The game has for Plasyer 2. In the backward induction equilibrium in pure strategies Player 2 gets a payott of subgames. The strategy profile (AGUKM, CED) leads to a payoff of for Player 1 and (Please, enter only numerical values like: 0. 1.2,3)
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