There are two firms in the residential paint industry, Cool Shades (C) and Warm Hues (W). They collude to share the market equally. They jointly set a monopoly price and split the quantity demanded at that price. Here are their options:

Question

i. They continue to collude (no cheating) and make $12 million each in profits.
ii. One firm cheats and the other does not. The firm that cheats makes a profit of $14 million whereas the firm that doesn't makes a profit of $9 million.
iii. They both cheat and each firm makes a profit of $7 million.

a. Construct a payoff matrix for these two firms.
b. How does this situation relate to the prisoner's dilemma?
c. If each firm acted noncooperatively, how much profit would each make?
d. Are the firms better off colluding (with no cheating) or competing? Explain.

Answer 1

a. The payoff matrix:

Cool Shades' (C) Strategies
Cheat Don't Cheat
Warm Hues' (W) Strategies Cheat C: $7 million
W: $7 million C: $9 million
W: $14 million
Don't Cheat C: $14 million
W: $9 million C: $12 million
W: $12 million

b. With a prisoner's dilemma, cooperative behavior - each prisoner standing firm without admitting to anything - leads to the best outcome for each player. But each player stands to gain by cheating. Similarly, in this case, each firm has the potential to make a profit of $14 million ($2 million above the outcome with collusion) if it unilaterally increases output. But if both acted on this incentive, then each ends up with only $7 million in profit. This outcome is inferior to cooperation.
c. Each firm has the potential to make a profit of $14 million if one cheats and the other does not. But if both cheat, then profits fall to $7 million each.
d. If they colluded (no cheating), each firm stands to make $12 million, an outcome which is superior to the cheating outcome.