Question

1. 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: 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 does not makes a profit of $9 million. iii. They both cheat and each firm makes a profit of $7 million.
   1. Construct a payoff matrix for these two firms.
   2. How does this situation relate to the prisoner's dilemma?
   3. If each firm acted noncooperatively, how much profit would each make?
   4. Are the firms better off colluding (with no cheating) or competing? Explain.

Answer 1

(a)

Payoff matrix (values in $ million).

		COOL SHADES
		Cheating	No Cheating
WARM HUES	Cheating	(7,   7)	(14,   9)
	No Cheating	(9,   14)	(12,   12)

(b)

If the firms do not collude and hence cheat, their individual and joint payoff are lower than the case if they collude and cheat (7 < 12, 7 < 12). This is therefore a prisoners' dilemma.

(c)

Non-cooperative (Nash) equilibrium is found as follows.

When Cool cheats, Warm's best strategy is to not cheat since payoff is higher (9 > 7).

When Cool doesn't cheat, Warm's best strategy is to cheat since payoff is higher (14 > 12).

When Warm cheats, Cool's best strategy is to not cheat since payoff is higher (9 > 7).

When Warm doesn't cheat, Cool's best strategy is to cheat since payoff is higher (14 > 12).

Therefore, Non-cooperative (Nash) equilibrium are: (Warm cheats, Cool doesn't cheat) & (Cool cheats, Warm doesn't cheat) [see below].

COOL SHADES Cheating No Cheating (7, 7) ( (14) 9) WARM Cheating No Cheating HUES 19014) (12, 12)

(d)

Firms are better off colluding since joint payoff is higher: (12 + 12) = 24 > (14 + 9) = 23.