Question

The next three questions will refer to the following game table:

			Player 2
		W	X	Y	Z
	A	1, 1	1, 2	2, 3	2, 4
Player 1	B	1, 2	2, 3	1, 4	4, 1
	C	2, 3	2, 4	1, 1	1, 2
	D	3, 4	3, 1	3, 2	2, 3

Q1. In the space below, answer the following questions:

• Does this game contain any strictly dominated strategies? (You do not need to list them right now.)
• If so, perform IESDS until none are left. List the order in which you eliminated strategies.

Q2. In the space below, answer the following questions:

• Does this game contain any non-rationalizable strategies? (You do not need to list them right now.)
• If so, perform IENBR until none are left. List the order in which you eliminated strategies.

Q3. In the space below, answer the following questions:

• Did either IESDS or IENBR, by themselves, reveal the Nash equilibrium of the game?
• What are the Nash equilibria of the game? (If they were not revealed by IESDS or IENBR, use any method you like to find them.)

Answer 1

	Player 2
Player 1		W	X	Y	Z
A	(1,1)	(1,2)	(2,3)	(2,4)
B	(1,2)	(2,3)	(1,4)	(4,1)
C	(2,3)	(2,4)	(1,1)	(1,2)
D	(3,4)	(3,1)	(3,2)	(2,3)

Question 1

If player 1 chooses A, Player 2 chooses Z

If player 1 chooses B, Player 2 chooses Y

If player 1 chooses C, Player 2 chooses X

If player 1 chooses D, Player 2 chooses W

NO DOMINANT STRATEGY FOR PLAYER 2

If player 2 chooses W, Player 1 chooses D

If player 2 chooses X, Player 1 chooses D

If player 2 chooses Y, Player 1 chooses D

If player 2 chooses Z, Player 1 chooses B

DOMINANT STRATEGY FOR PLAYER 1 IS D AND B.

Hence, after removal of A and C, we get -

	Player 2
Player 1		W	X	Y	Z
B	(1,2)	(2,3)	(1,4)	(4,1)
D	(3,4)	(3,1)	(3,2)	(2,3)

Now, again -

If player 1 chooses B, Player 2 chooses Y

If player 1 chooses D, Player 2 chooses W

Removing X and Z,

	Player 2
Player 1		W	Y
B	(1,2)	(1,4)
D	(3,4)	(3,2)

Now, again -

If player 2 chooses W, Player 1 chooses D

If player 2 chooses Y, Player 1 chooses D

Therefore, removing B

	Player 2
Player 1		W	Y
D	(3,4)	(3,2)

If Player 1 chooses D, player 2 will choose W.

Hence, dominant strategy is (D,W), Which is also the Nash Equilibrium of the game.