Question

2) Consider the scenario below: Two firms are merging into a larger company and must select a computer system for daily use. In the past, the players have used different systems I and A; each firm prefers the system it has used in the past. They will both be better off by using the same computer system than if they use different systems. The payoff matrix for the two players is given below:

Player 2

I

A

Player 1

I

2,1	0,0
0,0	1,2

A

1. Find the Nash equilibria of this game by considering all possibilities. Explain your answer fully.
2. Does the game depicted below have a Nash equilibrium? Why or why not?

Player

X

Y

Player 1

X

2,1	1,2
1,2	2,1

Y

Answer 1

a)

PLAYER 1 / PLAYER 2	I	A
I	2 , 1	0 , 0
A	0 , 0	1 , 2

If player 1 chooses I, then player 2 will choose I as it gives him a higher pay-off of 1 as compared to 0.

If player 1 chooses A, then player 2 will choose A as it gives him a higher pay-off of 2 as compared to 0.

If player 2 chooses I, then player 1 will choose I as it gives him a higher pay-off of 2 as compared to 0.

If player 2 chooses A, then player 1 will choose A as it gives him a higher pay-off of 1 as compared to 0.

So, (2,1) and (1,2) are the nash equilibrium in this case.

b)  

PLAYER 1 / PLAYER 2	X	Y
X	2 , 1	1 , 2
Y	1 , 2	2 , 1

If player 1 chooses X, then player 2 will choose Y as it gives a higher pay-off of 2 as compared to 1.

If player 1 chooses Y, then player 2 will choose X as it gives him a higher pay-off of 2 as compared to 1.

If player 2 chooses X, then player 1 will choose X as it gives him a higher pay-off of 2 as compared to 1.

If player 2 chooses Y, then player 1 will choose Y as it gives him a higher pay-off of 2 as compared to 1.

So, there is no nah equilibrium in this game because each player has a chance to deviate from his or her strategy if he gets a higher pay-off.