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Product differentiation, excess capacity, oligopoly models, game theory, and Nash equilibrium
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Most real-world markets fall between perfect competition and pure monopoly. The two most important intermediate structures are monopolistic competition and oligopoly.
Many sellers, but each offers a slightly differentiated product (think restaurants, hair salons, smartphone apps). Free entry and exit. Each firm has a small amount of market power because of differentiation, so its demand curve is downward-sloping (but more elastic than a pure monopolist's).
Short run: firm acts like a small monopolist. Sets , charges from demand, can earn positive profit, break even, or lose.
Long run: entry/exit drives economic profit to zero. The demand curve shifts until it is tangent to the ATC curve at the profit-maximizing . At this tangency:
In long-run equilibrium of monopolistic competition, what is the relationship between , , and at the profit-maximizing quantity?
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The trade-off society accepts: variety/differentiation in exchange for some inefficiency.
A few large firms dominate the market (auto, airlines, soft drinks, telecom). High barriers to entry. The defining feature is strategic interaction: each firm's optimal action depends on what rivals do. Tools include game theory and the kinked demand model.
A payoff matrix shows the outcomes for two firms based on each combination of strategies. A dominant strategy is the best move regardless of what the rival does. A Nash equilibrium is a combination where neither firm can improve by changing its own strategy unilaterally.
The classic Prisoners' Dilemma structure shows up in oligopolistic price wars and capacity decisions: each firm has a dominant strategy to "cheat" (cut price), leading to a Nash equilibrium worse for both than mutual cooperation.
Firms can earn higher profits by colluding (acting as a joint monopolist), but each then has an incentive to cheat by undercutting the cartel price. Cartels are unstable without enforcement — and most are illegal under antitrust law.
Real markets need these models. AP exam FRQs frequently ask you to (1) draw the long-run tangency for monopolistic competition, (2) construct or interpret a payoff matrix and identify dominant strategies and Nash equilibrium, and (3) explain why collusion is profitable but unstable.
At long-run equilibrium of monopolistic competition:
Below is a payoff matrix (Firm 1 row, Firm 2 column) of profits in millions:
| Low price | High price | |
|---|---|---|
| Low price | 5, 5 | 12, 2 |
| High price | 2, 12 | 10, 10 |
(a) Find each firm's dominant strategy. (b) Identify the Nash equilibrium. (c) What is the cooperative outcome both firms would prefer?
(a) Firm 1: If F2 plays Low → 5 vs 2 ⇒ Low is better. If F2 plays High → 12 vs 10 ⇒ Low is better. Low is dominant for F1. By symmetry, Low is dominant for F2.
(b) Nash equilibrium: both play Low ⇒ payoffs (5, 5). Neither can improve unilaterally.
(c) Both would prefer (High, High) → (10, 10), but each has an incentive to deviate to Low. Classic prisoners' dilemma — cooperation is jointly optimal but individually unstable.
Two pizza shops on a college campus engage in monopolistic competition and currently earn positive economic profit. Trace the long-run adjustment, and describe the position of the typical firm's demand curve relative to its ATC curve at the new equilibrium.
Adjustment:
Position of the demand curve at long-run equilibrium: Just tangent to ATC from above at the profit-maximizing . Above ATC nowhere ⇒ no profit; below ATC nowhere either ⇒ no losses driving exit.
Two firms in a duopoly are considering whether to invest in advanced R&D. Profits (millions):
| Invest | Don't invest | |
|---|---|---|
| Invest | 8, 8 | 14, 4 |
| Don't invest | 4, 14 | 10, 10 |
(a) Does either firm have a dominant strategy? (b) What is the Nash equilibrium? (c) Suppose investing also raises social welfare. Is the Nash equilibrium socially optimal?
(a) Firm 1: If F2 invests → 8 vs 4 ⇒ invest. If F2 doesn't → 14 vs 10 ⇒ invest. Investing is dominant for F1 (and for F2 by symmetry).
(b) Nash equilibrium: both invest ⇒ (8, 8).
(c) Social welfare and dominant strategy ALIGN here — both firms invest, the socially desirable outcome. Unlike the prisoners' dilemma, this game has no conflict between individual incentives and joint best outcome.
A cartel of 4 oil-producing countries agrees to restrict total output to keep prices high. (a) Why is each country's profit higher under the cartel than under unrestricted competition? (b) Why is the cartel unstable — describe the incentive any single member faces. (c) How does enforcement (e.g., monitoring, side payments) affect cartel stability?
(a) The cartel acts like a joint monopolist: it restricts to where , raising above competitive levels. Each member shares in higher monopoly profits compared to the zero-profit competitive outcome.
(b) Once price is high, any single member can SECRETLY expand output. That extra output earns the high cartel price (the deviator faces a more elastic individual demand than the cartel as a whole) so the deviator's profit RISES even further — at the expense of other members. Each member faces this same incentive ⇒ classic prisoners' dilemma at the cartel level.
(c) Monitoring detects cheating; enforcement (quotas, penalties, publication of production data, side payments) makes cheating costly. The more credibly cheating is punished, the longer the cartel can sustain high prices. OPEC's history is one long demonstration of this struggle — it works best when one large producer (Saudi Arabia) bears the cost of policing quotas.