Self Test

Finding Nash Equilibria

		Player 2
		X	Y
Player 1	A	10 , 10	15 , 5
Player 1	B	5 , 15	12 , 12

Question 1.

What is Player 1's best reply to Player 2 playing Y?

	none
	A
	B
	both A and B

Question 2.

What is the equilibrium of the above game?

	{A,X}
	{B,X}
	{A,Y}
	{B,Y}

Question 3.

Is {B,X} an equilibrium of the above game?

	Yes
	No, player 1 would deviate
	No, player 2 would deviate
	No, both players would deviate

Question 4.

		Player 2
		X	Y	Z
Player 1	A	5 , 5	1 , 1	4 , 8
Player 1	B	2 , 0	2 , 6	5 , 5

What are the equilibria of the above game?

	{A,X} only
	{A,X} and {B,Z}
	{B,Y} only
	{A,Z} only

Question 5.

		Player 2
		X	Y	Z
Player 1	A	6 , 6	8 , 20	0 , 8
	B	10 , 0	5 , 5	2 , 8
	C	8 , 0	20 , 0	4 , 4

What is the equilibrium of the above game?

	{B,Y}
	{C,Z}
	{A,X}
	{A,Y}

		Player 2
		L	R
Player 1	A	3 , 20	1 , 10
Player 1	D	2 , 10	0 , 30

Question 6.

How many equilibria does this game have?

	0
	1
	2
	3

Question 7.

For Player 1, what is true about strategy A?

	A is strictly dominant but not weakly dominant
	A is weakly dominant but not strictly dominant
	A is both strictly and weakly dominant
	A is not dominant

		Gilmour
		Lapse	Echoes	Bell
Waters	Wall	40 , 8	30 , 6	50 , 1
	Moon	30 , 6	20 , 9	50 , 1
	Wish	20 , 5	40 , 2	50 , 0

Question 8.

Does either player have a strictly dominant strategy?

	Waters only
	Gilmour only
	Both Waters and Gilmour
	Neither Waters nor Gilmour

Question 9.

Does either player have a weakly dominant strategy?

	Waters only
	Gilmour only
	Both Waters and Gilmour
	Neither Waters nor Gilmour

Question 10.

Does either player have a strictly dominated strategy?

	Waters only
	Gilmour only
	Both Waters and Gilmour
	Neither Waters nor Gilmour

Question 11.

Does either player have a weakly dominated strategy?

	Waters only
	Gilmour only
	Both Waters and Gilmour
	Neither Waters nor Gilmour

Question 12.

		Player 2
		X	Y
Player 1	A	0 , 0	0 , 1
Player 1	B	2 , 0	0 , 0

What are the equilibria of the above game?

	{B,X} only
	{A,Y} and {B,X}
	{A,Y}, {B,X}, and {B,Y}
	none

Question 13.

		Barney
		Left	Right
Fred	Up	10 , 10	0 , 10
Fred	Down	10 , 0	10 , 10

What are the equilibria of the above game?

	{Up,Left} only
	{Down,Right} only
	{Up,Left} and {Down,Right}
	{10,10}