. Player 1 and Player 2 are going to play the following stage game twice:
. 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 Nash of the stage game?
(b) Find a subgame perfect Nash equilibrium of the repeated game where the first time they play the stage game Player 1 chooses Top and Player 2 chooses Left.
Homework Answers
Add Answer to:
. Player 1 and Player 2 are going to play the following stage
game twice:
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...
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,...
Game: Extensive Form. Suppose player 1 chooses G or H, and player 2 observes this choice....
Game: Extensive Form. Suppose player 1 chooses G or H, and player 2 observes this choice. If player 1 chooses H, then player 2 must choose A or B. Player 1 does not get to observe this choice by player 2, and must then choose X or Y. If A and X are played, the payoff for player 1 is 1 and for player 2 it's 5. If A and Y are played, the payoff for player 1 is 6...
2. Consider the following sequential game. Player A can choose between two tasks, Tl and T2....
2. Consider the following sequential game. Player A can choose between two tasks, Tl and T2. After having observed the choice of A, Player B chooses between two projects Pl or P2. The payoffs are as follows: If A chooses TI and B chooses P1 the payoffs are (12, 8), where the first payoff is for A and the second for B; if A chooses T1 and B opts for P2 the payoffs are (20, 7); if A chooses T2...
2. Consider the following sequential game. Player A can choose between two tasks, TI and T2....
2. Consider the following sequential game. Player A can choose between two tasks, TI and T2. After having observed the choice of A, Player B chooses between two projects P1 or P2. The payoffs are as follows: If A chooses TI and B chooses Pl the payoffs are (12.8), where the first payoff is for A and the second for B; if A chooses TI and B opts for P2 the payoffs are (20,7); if A chooses T2 and B...
1. Consider the following normal form game: 112 L CR T 10 102 12 0 13...
1. Consider the following normal form game: 112 L CR T 10 102 12 0 13 M 12 25 5 0 0 B|13 010 011 a) (Level A) First suppose this game is played only once. What are the pure strategy Nash equilibria? (b) (Level B) Now suppose this game is played twice. Players observe the actions chosen in the first period prior to the second period. Each player's total payoff is the sum of his/her payoff in the two...
1. Consider the following normal form game 112 L CR T|10 1012 1210 13 M 12...
1. Consider the following normal form game 112 L CR T|10 1012 1210 13 M 12 25 5 0 (0 B113 0100 (a) (Level A) First suppose this game is played only once. What are the pure strategy Nash equilibria? (b) (Level B) Now suppose this game is played twice. Players observe the actions chosen in the first period prior to the second period. Each player's total payoff is the sum of his/her payoff in the two periods. Consider the...
2. Consider the extensive form game shown in the figure below. The top payoff at a terminal node ...
2. Consider the extensive form game shown in the figure below. The top payoff at a terminal node is for player 1. Find all subgame perfect Nash equilibria P1 P2 P2 P1 P1 0 10 4 4 4
2. Consider the extensive form game shown in the figure below. The top payoff at a terminal node is for player 1. Find all subgame perfect Nash equilibria P1 P2 P2 P1 P1 0 10 4 4 4
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...
Consider the infinitely repeated version of the symmetric two-player stage game in figure PR 13.2. The first number in a cell is player 1's single-period payoff. Assume that past actions are commo...
Consider the infinitely repeated version of the symmetric
two-player stage game in figure PR 13.2. The first number in a cell
is player 1's single-period payoff. Assume that past actions are
common knowledge. Each player's payoff is the present value of the
stream of single-period payoffs where the discount factor is d. (a)
Derive the conditions whereby the following strategy profile is a
subgame perfect Nash Equilibrium:
2 Consider the infinitely repeated version of the symmetric two-player stage game in...
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...
2. Consider the following sequential game. Player A can choose between two tasks, Tl and T2. After having observed the choice of A, Player B chooses between two projects Pl or P2. The payoffs are as follows: If A chooses TI and B chooses P1 the payoffs are (12, 8), where the first payoff is for A and the second for B; if A chooses T1 and B opts for P2 the payoffs are (20, 7); if A chooses T2...
2. Consider the following sequential game. Player A can choose between two tasks, TI and T2. After having observed the choice of A, Player B chooses between two projects P1 or P2. The payoffs are as follows: If A chooses TI and B chooses Pl the payoffs are (12.8), where the first payoff is for A and the second for B; if A chooses TI and B opts for P2 the payoffs are (20,7); if A chooses T2 and B...
1. Consider the following normal form game: 112 L CR T 10 102 12 0 13 M 12 25 5 0 0 B|13 010 011 a) (Level A) First suppose this game is played only once. What are the pure strategy Nash equilibria? (b) (Level B) Now suppose this game is played twice. Players observe the actions chosen in the first period prior to the second period. Each player's total payoff is the sum of his/her payoff in the two...
1. Consider the following normal form game 112 L CR T|10 1012 1210 13 M 12 25 5 0 (0 B113 0100 (a) (Level A) First suppose this game is played only once. What are the pure strategy Nash equilibria? (b) (Level B) Now suppose this game is played twice. Players observe the actions chosen in the first period prior to the second period. Each player's total payoff is the sum of his/her payoff in the two periods. Consider the...
2. Consider the extensive form game shown in the figure below. The top payoff at a terminal node is for player 1. Find all subgame perfect Nash equilibria P1 P2 P2 P1 P1 0 10 4 4 4
2. Consider the extensive form game shown in the figure below. The top payoff at a terminal node is for player 1. Find all subgame perfect Nash equilibria P1 P2 P2 P1 P1 0 10 4 4 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...
Consider the infinitely repeated version of the symmetric
two-player stage game in figure PR 13.2. The first number in a cell
is player 1's single-period payoff. Assume that past actions are
common knowledge. Each player's payoff is the present value of the
stream of single-period payoffs where the discount factor is d. (a)
Derive the conditions whereby the following strategy profile is a
subgame perfect Nash Equilibrium:
2 Consider the infinitely repeated version of the symmetric two-player stage game in...
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