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 


A 
Player 

X 
Y 

Player 1 
X 


Y 
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 payoff of 1 as compared to 0.
If player 1 chooses A, then player 2 will choose A as it gives him a higher payoff of 2 as compared to 0.
If player 2 chooses I, then player 1 will choose I as it gives him a higher payoff of 2 as compared to 0.
If player 2 chooses A, then player 1 will choose A as it gives him a higher payoff 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 payoff of 2 as compared to 1.
If player 1 chooses Y, then player 2 will choose X as it gives him a higher payoff of 2 as compared to 1.
If player 2 chooses X, then player 1 will choose X as it gives him a higher payoff of 2 as compared to 1.
If player 2 chooses Y, then player 1 will choose Y as it gives him a higher payoff 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 payoff.
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