Question

onsider the following two person static game where Player 1 is the row player and Player 2 is the column player

	C	D	E
A	1,1	0,2	2,0
B	0,0	1,-1	-1,3

	a.	There is an equilibrium where Player 1 plays A with probability 3/4.
	b.	There is an equilibrium where Player 1 plays A with probability 2/3.
	c.	There is an equilibrium where Player 1 plays A with probability 1/2.
	d.	There is no mixed strategy Nash equilibrium.

Answer 1

	C	D	E
A	1 1	0 2	2 0
B	0 0	1 -1	-1 3

We assign probability p and 1-p to strategy A and B respectively of Player 1. Similarly, we assign probability of q1 , q2 and 1-q1-q2 to strategy C , D and E respectively of Player 2.

To derive the mixed strategy nash equilibrium: we need to calculate the expected pay off of the players.

Player 1 chooses probability p such that player 2 is indifferent between C and D

Thus,

p. (1) + 1-p (0) = p(2)+1-p(-1)

p=2p-1+p

p-3p = -1

p=1/2

Similarly, Player 1 chooses probability p such that player 2 is indifferent between D and E

p(2)+1-p(-1) = p(0) + 1-p (3)

2p-1+p= 3-3p

3p-1= 3-3p

6p = 4

p=2/3

This is impossible. Therefore we donot have mixed strategy naash equilibrium for this game