Question 1.    (10 points)

Player 2

Player 1

A

B

C

L                     M                     R

a.   (5 points) Use the iterated elimination of dominated strategies (IEDS) to reduce the game matrix as far as possible. You must label the steps of your elimination to indicate which is 1st step, 2nd    step, etc. Hint: 1st check if a player has a strategy that is strictly dominated by another pure         strategy (try this on both players). If not, then check if any player has a strategy that is strictly    dominated by a mixed strategy.

b.   (5 points) In the reduced game, find all Nash equilibria to this game, including mixed-strategy Nash equilibria.

Question 2.    (23 points)

Consider the following game tree with two players: 1 and 2. Focus on pure strategy only (do not use mixed strategy):

a.   (2 points) How many information sets does each player have?

b.   (2 points) How many strategies does each player have?

c.   (2 points) How many strategy profiles are there in this game?

d.   (4 points) How many subgames are there in this game? Circle all proper subgames in the above game tree

e.   (13 points) Find all the subgame perfect Nash equilibria.

8,6

1

W

6,0

A

9,4

1 

D

12,1

20,10

2

Z

10,15