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?

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
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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?
Transcribed Image Text: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?
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