Question

1. Consider the following normal form game:

1\2	X	Y	Z
A	3,3	0,5	0,4
B	0,0	3,1	1,2
C	-1,5	2,2	0,1

a. Does the game have a dominant strategy solution? If yes, which one? (no proof needed) (10 pts)

                                                                                                        

b. Does the game have a solution to IEDS? What is it? Show your procedure. (10 pts)

Answer 1

a. There is no dominant strategy solution.
Given that 2 choose X, 1's best response is A(3).
Given that 2 choose Y, 1's best response is B(3).
Given that 2 choose Z, 1's best response is B(1).
So, 1 does not have any dominant strategy and thus there is no dominant strategy solution.

b. As 1 never choose C, so C can be eliminated. Thus game reduces to

1\2	X	Y	Z
A	3,3	0,5	0,4
B	0,0	3,1	1,2

Now, given that 1 choose A, 2's best response is Y(5).
Given that 1 choose B, 2's best response is Z(2).
So, 2 never choose X. Thus X is eliminated and game reduces to:

1\2		Y	Z
A		0,5	0,4
B		3,1	1,2

Now, Given that 2 choose Y, 1's best response is B(3).
Given that 2 choose Z, 1's best response is B(1).
So, 1 never choose A. Thus, A is eliminated. So, the game reduces to:

1\2		Y	Z
B		3,1	1,2

Now, 2 will choose Z(2).
So, Y is eliminated. And the outcome is (B, Z) = (1, 2)