Question

Consider the following game between Bobbi and Gary:

			Gary
		Left	Center	Right
	High	4, 4	7, 5	5, 2
Bobbi	Middle	8, 3	2, 4	1, 12
	Low	10, 6	9, 1	4, 3

1. T/F Gary has a dominant strategy.

2. T/F  Bobbi has a dominant strategy.

3. Does Gary have a dominated strategy? If so, what is it?

4. Does Bobbi have a dominated strategy? If so, what is it?

5. What is Gary's choice in the Nash Equilibrium?

6. What is Bobbi's choice in the Nash Equilibrium?

Answer 1

for a dominant strategy , a player should get the highest payoff from only that strategy, for any choice of other player.

1. Gary does not have a dominant strategy because if he plays Left then gets pay-off (4,3,6) and if play Center, then gets (5,4,1). Now, 5> 4, 4> 3 but 1 is not greater than 6.

Similarly, If he plays Right, then payoff (2,12,3). Now, Comparing Left and Right. 4>2 , But 3 is not greater than 12.

Statement is False.

2.

True. Bobbi has a dominant strategy which is "Low"

Payoff if Low is played: (10,9,4)

Payoff if Middle is played: ((8,2,1)

10 > 8 , 9 > 2 and 4 > 1

So, statement is TRUE

3

Gary does not have any dominated strategy

4.

Yes.

Dominated strategy of Bobbi: Middle

5.

	High	Middle	Low
High	(4,4)	(7,5)%	(5,2)%
Middle	(8,3)	(2,4)	(1,12)%
Low	(10,6)%#	(9,1)#	(4,3)

Nash Equilibrium of the game is (Low, High)

Gary's choice is "High"

6.

Bobbi choice is "Low" in nash equilibrium