# Represent in a diagram the two-player extensive game with perfect information in which the terminal histories

## Assignment 5: Due Wednesday October 28, 2015 at the BEGINNING

Assignment 5: Due Wednesday October 28, 2015 at the BEGINNING

Question
E327 Game Theory
Assignment 5: Due Wednesday October 28, 2015 at the BEGINNING of class
1. Consider the following (2×3) strategic game.
Player 2Player 1

Left

Center

Right

Top

4,2

0,0

0,1

Bottom

0,0

2,4

1,3

Find all the mixed-strategy Nash equilibria of this game by the “brute force method”, i.e. use Proposition 116.2 in your textbook.
2. Consider the following (2×3) strategic game.
Player 2

Player 1

Left

Center

Right

Top

2,2

0,3

1,2

Bottom

3,1

1,0

0,2

Find all the mixed-strategy Nash equilibria of this game by ﬁrst eliminating any strictly dominated
actions and then constructing the players’ best response functions.

3.

(a)

## Assignment 5: Due Wednesday October 28, 2015 at the BEGINNING

Assignment 5: Due Wednesday October 28, 2015 at the BEGINNING

Question
E327 Game Theory
Assignment 5: Due Wednesday October 28, 2015 at the BEGINNING of class
1. Consider the following (2×3) strategic game.
Player 2Player 1

Left

Center

Right

Top

4,2

0,0

0,1

Bottom

0,0

2,4

1,3

Find all the mixed-strategy Nash equilibria of this game by the “brute force method”, i.e. use Proposition 116.2 in your textbook.
2. Consider the following (2×3) strategic game.
Player 2

Player 1

Left

Center

Right

Top

2,2

0,3

1,2

Bottom

3,1

1,0

0,2

Find all the mixed-strategy Nash equilibria of this game by ﬁrst eliminating any strictly dominated
actions and then constructing the players’ best response functions.

3.

(a) Represent in a diagram the two-player extensive game with perfect information in which the terminal histories are (C, E), (C, F ), (D, G), and (D, H), the player function is given by P (∅) = 1
and P (C) = P (D) = 2. Player 1 prefers (C, F ) to (D, G) to (C, E) to (D, H) and player 2 prefers
(D, G) to (C, F ) to (D, H) to (C, E).
(b) List all of player 1’s possible strategies.
(c) List all of player 2’s possible strategies.
(d) List all possible strategy proﬁles and their corresponding outcomes and payoﬀs.
(e) Find all Nash equilibria of the above game.
(f) Find all subgame perfect equilibria of the above game.

1

4. Two people select a policy that aﬀects them both by alternately vetoing policies until only one remains.
First person 1 vetoes a policy. If more than one policy remains, person 2 then vetoes a policy. If more
than one policy still remains, person 1 then vetoes another policy. The process continues until a single
policy remains unvetoed. Suppose there are three possible policies, X, Y, and Z. Person 1 prefers X to
Y to Z, and person 2 prefers Z to Y to X.
(a) Model this situation as an extensive game and ﬁnd its Nash equilibria.
(b) Which of these Nash equilibria are subgame perfect?

2

Assignment 5: Due Wednesday October 28, 2015 at the BEGINNING

are (C, E), (C, F ), (D, G), and (D, H), the player function is given by P (∅) = 1
and P (C) = P (D) = 2. Player 1 prefers (C, F ) to (D, G) to (C, E) to (D, H) and player 2 prefers
(D, G) to (C, F ) to (D, H) to (C, E).
(b) List all of player 1’s possible strategies.
(c) List all of player 2’s possible strategies.
(d) List all possible strategy proﬁles and their corresponding outcomes and payoﬀs.
(e) Find all Nash equilibria of the above game.
(f) Find all subgame perfect equilibria of the above game.

1

4. Two people select a policy that aﬀects them both by alternately vetoing policies until only one remains.
First person 1 vetoes a policy. If more than one policy remains, person 2 then vetoes a policy. If more
than one policy still remains, person 1 then vetoes another policy. The process continues until a single
policy remains unvetoed. Suppose there are three possible policies, X, Y, and Z. Person 1 prefers X to
Y to Z, and person 2 prefers Z to Y to X.
(a) Model this situation as an extensive game and ﬁnd its Nash equilibria.
(b) Which of these Nash equilibria are subgame perfect?

2

Assignment 5: Due Wednesday October 28, 2015 at the BEGINNING

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