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