Answer Happy

In a duopoly, firm X and firm Y decide to collude on setting a
high price. If both firms cooperate by charging the high price,
they can both make high profits of $50 million each. If one of the
firms decides to cheat and undercut it’s competitor by lowering
price (while the competitor does not cheat and charges the
agreed-upon high price), then it can make very high profits since
it will gain market share at the expense of the competitor – the
cheating firm will earn $80 million while the non-cheating firm
will suffer a loss of $10 million. If both firms cheat and set a
low price, then they will both make lower profits of $30 million
each. The payoffs for the firms are shown in the matrix below.
Charge High Price Charge Low Price Charge High Price $50, $50 −$10,
$80 Charge Low Price $80, −$10 $30, $30 a. What is the dominant
strategy for Firm X? What is the dominant strategy for Firm Y?
b. Find the Nash equilibrium, including the payoffs that each
firm makes in the equilibrium?