4.5 - Oligopoly and Game Theory
Characteristics
An oligopoly is dominated by a small handful of players:
- Few sellers: typically fewer than 10.
- High entry barriers: steep startup costs, heavy regulation, strong customer loyalty.
- Mutual interdependence: with so few firms, each one’s actions directly affect the others, forcing strategic thinking about how rivals will react.
- Examples: cell phone carriers, airlines.
Efficiency
Oligopolies fail the efficiency test, just like monopolies:
- Allocative inefficiency: price above marginal cost, lower output, higher price than competitive markets, creating deadweight loss.
- Productive inefficiency: production happens on the downward-sloping part of ATC, not at its minimum.
Game Theory and the Payoff Matrix
Because oligopolists are interdependent, economists use game theory, especially the payoff matrix, to model behavior between two firms (a duopoly).
- Game: any situation where each player’s payoff depends on both their own choice and the choices of the others. Two firms setting prices are playing a game, since each firm’s profit depends on what the other charges.
- Strategies: usually something like “raise price” or “lower price.”
- A strategy is a player’s complete plan of action for the game. In a payoff matrix, each firm just picks one of its two choices.
- Reading payoffs: in each box, the first number belongs to the firm on the left, the second to the firm on top.
- Normal form: a payoff matrix is the normal form of a game, a table that shows the payoffs for every combination of strategies (one for each player). On the AP exam, games have two players with two strategies each.
Key outcomes:
- Collusion (the monopoly outcome): the best combined result for both firms, found in the quadrant with the highest total profit. It’s profitable, but generally illegal under antitrust law.
- Cartel: a group of firms that formally agrees to act like a single monopoly, setting a high price and splitting up the lower output. Oligopolists have a strong incentive to collude this way, since together they can earn the monopoly profit. Example: OPEC, a group of oil-exporting countries that sets production limits for its members. Cartels are illegal in the US (the Sherman Antitrust Act), and they tend to fall apart because each member can earn more by secretly cheating, cutting its price or producing more than its share.
- Dominant strategy: whatever a firm would do no matter what its rival does. Check the firm’s best response to every possible rival move, if the answer’s always the same, that’s the dominant strategy.
- Nash equilibrium: the most likely real-world outcome, where neither firm benefits from changing its strategy alone. A matrix can sometimes have two Nash equilibria.
Example: Solving a Payoff Matrix
Two firms, A and B, each choose a high or low price. The numbers are profits in dollars, with Firm A’s payoff first.
Firm B: High Price | Firm B: Low Price | |
Firm A: High Price | 600, 600 | 200, 750 |
Firm A: Low Price | 750, 200 | 300, 300 |
- Firm A’s dominant strategy: if B picks High, A earns 600 with High or 750 with Low, so Low is better. If B picks Low, A earns 200 with High or 300 with Low, so Low is better again. Low wins no matter what B does, so Low Price is A’s dominant strategy.
- Firm B’s dominant strategy: the payoffs are the same from B’s side (750 > 600 and 300 > 200), so Low Price is B’s dominant strategy too.
- Nash equilibrium: both charge Low (300, 300). If A switched to High on its own, its profit would drop from 300 to 200, and the same is true for B. Neither firm can do better by changing alone.
- Collusive outcome: both charge High (600, 600), the box with the highest total profit (1,200). It isn’t a Nash equilibrium, though: if B charges High, A can earn 750 instead of 600 by switching to Low, and B is tempted the same way.
The Prisoner’s Dilemma
The game above is a prisoner’s dilemma: each player follows its dominant strategy, and both end up worse off (300 each) than if they had cooperated (600 each).
- The original (non-market) story: two suspects are questioned in separate rooms, and each can stay quiet or confess. Whatever the other one does, confessing gets a suspect a lighter sentence, so confessing is a dominant strategy. Both confess, and both get longer sentences than if they had both stayed quiet.
- Why oligopolies struggle to collude: the same thing happens to oligopolists. The monopoly outcome (everyone charging High) is best for the group, but each firm can earn more by cheating, so cartels and secret deals are hard to hold together.
- Result: prices in an oligopoly are still generally higher and quantities lower than in perfect competition, even though the firms usually don’t reach the full monopoly outcome.
Changing a Dominant Strategy
AP questions often ask how big an incentive (a fine, tax, or bonus) would have to be to change a player’s dominant strategy. Using the matrix above: suppose Firm A has to pay a fine every time it charges the low price. How big does the fine need to be for High Price to become A’s dominant strategy?
- Find how much Low beats High for Firm A in each column. If B picks High: 750 − 600 = 150. If B picks Low: 300 − 200 = 100.
- For High to be dominant, it has to win in both columns, so the fine has to cover the bigger gap. The fine must be more than $150.
- Check: with a $160 fine, A’s Low payoffs drop to 590 and 140. Now High wins either way (600 > 590 and 200 > 140).
A fine of exactly $150 isn’t enough, since A would be indifferent when B picks High. A smaller fine, like $120, leaves A with no dominant strategy at all: A would pick High if B picks Low (200 > 180) but still pick Low if B picks High (630 > 600). A bonus for charging High works the same way: it would also have to be more than $150.
Bottom line: oligopolies play out like a strategic chess match between a few powerful firms. Since profits are interdependent, they often face a prisoner’s dilemma: collusion is the best group outcome, but hard to sustain since each firm has an incentive to cheat for a better personal payoff. The market usually settles at a Nash equilibrium, stable, but inefficient for society.