Nash equilibrium and dominant strategy.
1. Suppose two competitors, Coa, Inc., and Han, Inc., are locked in a bitter pricing struggle in the aluminum industry. In the limit pricing payoff matrix, Coa can choose a given row of outcomes by offering a limit price ("up") or monopoly price ("down"). Han can choose a given column of outcomes by choosing to offer a limit price ("left") or monopoly price ("right"). Neither firm can choose which cell of the payoff matrix to obtain; the payoff for each firm depends upon the pricing strategies of both firms.


Han 


Pricing Strategy 
Limit Price 
Monopoly Price 
Coa 
Limit Price 
$1.5 billion, $3 billion 
$2.5 billion, $2 billion 

Monopoly Price 
$1 billion, $4 billion 
$1.75 billion, $3 billion 
A. Is there dominant strategy equilibrium in this problem? If so, what is it?
B. Is there Nash equilibrium in this problem? If so, what is it?
2. A hypothetical monopoly firm is characterized by the following diagram:
a. Assuming that the above firm is a profit maximizes operating in the short run, determine its optimal price?
b. Describe the firm's profit per unit.
c. What is the ATC in dollars?
d. If the above monopolist were to behave like a perfectly competitive firm (operating in the long run), determine its price.