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Consider the 2x2 game below: Left Right Top (4,5) (3, 2) Bottom (5,2) (2,6) In the...
1. (20 points) Consider the following game: Left 7,17 10,5 4,4 Top Middle Bottom Player B...
1. (20 points) Consider the following game: Left 7,17 10,5 4,4 Top Middle Bottom Player B Middle 21,21 14,4 7,3 Right 14,11 4,3 10,25 Player A a. Does either player have a dominant strategy? What about a dominated strategy? b. What are the Nash equilibria of this game? C. Is there one Nash equilibrium that you think is a more likely outcome than the others? If so, why? If not, why not? d. Now suppose the game looks like this:...
3. (30 pts) Consider the following game. Players can choose either left () or 'right' (r) The tab...
3. (30 pts) Consider the following game. Players can choose either left () or 'right' (r) The table provided below gives the payoffs to player A and B given any set of choices, where player A's payoff is the firat number and player B's payoff is the second number Player B Player A 4,4 1,6 r 6,1 -3.-3 (a) Solve for the pure strategy Nash equilibria. (4 pta) (b) Suppose player A chooses l with probability p and player B...
2. Consider the following simultaneous move game: Column Left Right Top 1,1 7,3 Row Bottom 3,5...
2. Consider the following simultaneous move game: Column Left Right Top 1,1 7,3 Row Bottom 3,5 11,0 (a) Find all pure-strategy Nash equilibria (b) Now assume that the game is made sequential with Row moving first. Illustrate this new game using a game tree and find the rollback equilibrium (c) List the strategies of the two players in this sequential-move game and give the normal-form representation of the game (the payoff matrix) (d) Use the payoff matrix to find the...
3. Player 1 and Player 2 are going to play the following stage game twice: &n...
3. Player 1 and Player 2 are going to play the following stage
game twice:
Player 2
Left
Middle
Right
Player 1
Top
4, 3
0, 0
1, 4
Bottom
0, 0
2, 1
0, 0
There is no discounting in this problem and so a player’s payoff
in this repeated game is the sum of her payoffs in the two plays of
the stage game.
(a) Find the Nash equilibria of the stage game. Is (Top, Left) a...
Suppose that two players are playing the following game
Suppose that two players are playing the following game. Player 1 can choose either top or bottom, and Player 2 can choose either left of right. The payoffs are given in the following table Player 2 Left Right top 9,4 2,3 Player 1 Bottom 1,0 3,1 where the number on the left is the payoff to Player 1 and the number on the right is the payoff to player 2. 1) Determine the nash equilibrium of the game. 2) If...
NEED WITHIN THE HOUR! Suppose that two players are playing the following game. Player A can...
NEED WITHIN THE HOUR!
Suppose that two players are playing the following game. Player
A can choose either Top or Bottom, and Player B can choose either
Left or Right. The payoffs are given in the following table where
the number on the left is the payoff to Player A, and the number on
the right is the payoff to Player B.
Does Player A have a dominant strategy? If so, what is it?
Group of answer choices
Top is...
1. Basic Game Theory (21 points) Consider the following game Player Top Bottom Left 21, 23 22. 16 Player 2 Right 20...
1. Basic Game Theory (21 points) Consider the following game Player Top Bottom Left 21, 23 22. 16 Player 2 Right 20, 24 19. 18 A. (6 points) Does player 2 have a dominant strategy. If yes, describe it B. (9 points) Can this game be solved by the elimination of dominated strategy? If yes, describe your method and result in detail C. (6 points) Now suppose there is some change to the payoff matrix, find the Nash equilibrium for...
GAME MATRIX Consider two players (Rose as player 1 and Kalum as player 2) in which each player has 2 possible actions (...
GAME MATRIX
Consider two players (Rose as player 1 and Kalum as player 2) in which each player has 2 possible actions (Up or Down for Rose; Left or Right for Kalum. This can be represented by a 2x2 game with 8 different numbers (the payoffs). Write out three different games such that: (a) There are zero pure-strategy Nash equilibria. (b) There is exactly one pure-strategy equilibrium. (c) There are two pure-strategy Nash equilibria.
Consider two players (Rose as player...
2. consider the following simultaneous move game. Player B LEFT RIGHT Player A UP 4,1 1,4...
2. consider the following simultaneous move game. Player B LEFT RIGHT Player A UP 4,1 1,4 DOWN 2,3 3,2 a. If there is a Nash equilibrium in pure strategies, what is it and what are the payoffs? b. If there is a Nash equilibrium in mixed strategies, what is it and what are the expected payoffs? 3. Continue with the previous game but suppose this was a sequential game where Player A got to go first. a. Diagram the game...
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...
1. (20 points) Consider the following game: Left 7,17 10,5 4,4 Top Middle Bottom Player B Middle 21,21 14,4 7,3 Right 14,11 4,3 10,25 Player A a. Does either player have a dominant strategy? What about a dominated strategy? b. What are the Nash equilibria of this game? C. Is there one Nash equilibrium that you think is a more likely outcome than the others? If so, why? If not, why not? d. Now suppose the game looks like this:...
3. (30 pts) Consider the following game. Players can choose either left () or 'right' (r) The table provided below gives the payoffs to player A and B given any set of choices, where player A's payoff is the firat number and player B's payoff is the second number Player B Player A 4,4 1,6 r 6,1 -3.-3 (a) Solve for the pure strategy Nash equilibria. (4 pta) (b) Suppose player A chooses l with probability p and player B...
2. Consider the following simultaneous move game: Column Left Right Top 1,1 7,3 Row Bottom 3,5 11,0 (a) Find all pure-strategy Nash equilibria (b) Now assume that the game is made sequential with Row moving first. Illustrate this new game using a game tree and find the rollback equilibrium (c) List the strategies of the two players in this sequential-move game and give the normal-form representation of the game (the payoff matrix) (d) Use the payoff matrix to find the...
3. Player 1 and Player 2 are going to play the following stage
game twice:
Player 2
Left
Middle
Right
Player 1
Top
4, 3
0, 0
1, 4
Bottom
0, 0
2, 1
0, 0
There is no discounting in this problem and so a player’s payoff
in this repeated game is the sum of her payoffs in the two plays of
the stage game.
(a) Find the Nash equilibria of the stage game. Is (Top, Left) a...
NEED WITHIN THE HOUR!
Suppose that two players are playing the following game. Player
A can choose either Top or Bottom, and Player B can choose either
Left or Right. The payoffs are given in the following table where
the number on the left is the payoff to Player A, and the number on
the right is the payoff to Player B.
Does Player A have a dominant strategy? If so, what is it?
Group of answer choices
Top is...
1. Basic Game Theory (21 points) Consider the following game Player Top Bottom Left 21, 23 22. 16 Player 2 Right 20, 24 19. 18 A. (6 points) Does player 2 have a dominant strategy. If yes, describe it B. (9 points) Can this game be solved by the elimination of dominated strategy? If yes, describe your method and result in detail C. (6 points) Now suppose there is some change to the payoff matrix, find the Nash equilibrium for...
GAME MATRIX
Consider two players (Rose as player 1 and Kalum as player 2) in which each player has 2 possible actions (Up or Down for Rose; Left or Right for Kalum. This can be represented by a 2x2 game with 8 different numbers (the payoffs). Write out three different games such that: (a) There are zero pure-strategy Nash equilibria. (b) There is exactly one pure-strategy equilibrium. (c) There are two pure-strategy Nash equilibria.
Consider two players (Rose as player...
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...
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