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Oligopoly &
Game Theory

Explore how a few dominant firms make strategic decisions, why interdependence shapes market outcomes, and how the Prisoner's Dilemma reveals the logic of competition and collusion.

AP Microeconomics

What Is an Oligopoly?

An oligopoly is a market structure dominated by a small number of large firms. Each firm holds enough market power that its decisions on price, output, and strategy directly affect its rivals. This mutual interdependence is the defining feature that separates oligopoly from all other market structures.

Few Sellers
The market is controlled by a handful of firms, each with significant share.
Interdependence
Each firm must consider rival reactions before making decisions.
Barriers to Entry
High startup costs, patents, or brand loyalty keep new firms out.

Why Oligopoly Matters

Most real-world industries are oligopolies: airlines, smartphones, automobiles, streaming services, and soft drinks. Unlike perfect competition, firms in an oligopoly face a strategic environment where every move triggers a counter-move.

Foundations of Game Theory

Game theory is the study of strategic interactions where the outcome for each participant depends on the actions of all participants. Every game has three essential components:

1
Players: The decision-makers: typically two or more firms in an oligopoly.
2
Strategies: The possible actions each player can choose (e.g., set a high price or a low price).
3
Payoffs: The profit (or loss) each player receives for every combination of strategies.

The Prisoner's Dilemma

The Prisoner's Dilemma is the most famous game in economics. Two firms (or prisoners) each choose to cooperate or defect. The dilemma: individual incentives push both to defect, even though mutual cooperation would make both better off.

Cooperate Defect Cooperate Defect FIRM A FIRM B $8M $8M Both profit well $2M $10M B exploits A $10M $2M A exploits B $5M $5M ★ Nash Equilibrium ■ Firm A payoff ■ Firm B payoff

Finding the Dominant Strategy

A dominant strategy is one that yields the highest payoff for a player regardless of what the other player chooses. If both players have a dominant strategy, the game has a clear, predictable outcome.

1
Fix Firm B's choice at "Cooperate": Firm A earns $8M by cooperating or $10M by defecting. Defecting is better.
2
Fix Firm B's choice at "Defect": Firm A earns $2M by cooperating or $5M by defecting. Defecting is still better.
3
Conclusion: "Defect" is Firm A's dominant strategy. By symmetry, "Defect" is also Firm B's dominant strategy.

Nash Equilibrium: The Core Concept

A Nash Equilibrium occurs when no player can improve their payoff by unilaterally changing their strategy, given the other player's strategy. It is the stable resting point of a game.

Definition
A set of strategies where each player's choice is a best response to the other's choice.
Stability
Once reached, neither player has incentive to deviate: any switch would lower their own payoff.

Collusion vs. Competition

Oligopolists face a fundamental tension: they would all profit more by colluding (acting like a monopoly), but each firm has an individual incentive to cheat on any agreement.

Collusion (Cartel)
Firms agree to restrict output and raise prices together. Acts like a shared monopoly. Joint profits are maximized.
Cheating (Defection)
A firm secretly undercuts the agreed price to steal market share. Short-term gains are large, but trust collapses.

How to Solve a Payoff Matrix

1
Identify the players, strategies, and payoffs. Read the matrix carefully: the first number in each cell is typically Player A's payoff, and the second is Player B's.
2
Find each player's best response. Fix one player's strategy, then find the other player's highest payoff. Circle or underline it. Repeat for every combination.
3
Check for dominant strategies. If one strategy is best for a player in every column (or row), it is that player's dominant strategy.
4
Locate the Nash Equilibrium. The cell where both players' best responses coincide is the Nash Equilibrium. Neither player would deviate unilaterally.

Worked Example: Pricing Game

Two airlines, Alpha and Beta, each choose to set a High or Low fare. Payoffs are monthly profits in millions:

BETA A L P H A High Fare Low Fare High Fare Low Fare $12M $12M $4M $16M $16M $4M $8M $8M ★ Nash Equilibrium ■ Alpha's payoff ■ Beta's payoff

Example: No Dominant Strategy

Not all games have dominant strategies. Consider two tech companies choosing between Innovate and Imitate:

FIRM Y FIRM X Innovate Imitate Innovate Imitate $0M $0M $6M $1M ★ Nash $1M $6M ★ Nash $2M $2M ■ Firm X ■ Firm Y

Example: Cartel vs. Cheating

Two oil producers agree to each produce 100 barrels/day at a price of $80/barrel. If one cheats and produces 150 barrels, the cheater earns $9,000 while the cooperator's profit falls to $5,000. If both cheat (each producing 150), price falls so each earns $6,000.

1
Both cooperate: Each earns \(100 \times \$80 = \$8,000\)/day
2
One cheats, one cooperates: Cheater earns $9,000. Cooperator earns $5,000.
3
Both cheat: Each earns $6,000/day

Repeated Games and Cooperation

The Prisoner's Dilemma looks grim, but most oligopolies play the game repeatedly. When firms interact over time, cooperation can emerge through credible threats of punishment.

Tit-for-Tat
Start by cooperating. Then mirror whatever the rival did last round. Simple, forgiving, and retaliatory.
Trigger Strategy
Cooperate until a rival cheats, then defect forever. The threat of permanent punishment deters cheating.
Grim Trigger
Extreme version of trigger: one defection causes all firms to revert to Nash Equilibrium permanently.

The Kinked Demand Curve Model

The kinked demand curve model explains why oligopoly prices tend to be sticky (resistant to change). The key assumption: rivals match price decreases but ignore price increases.

Price Quantity \(P^*\) \(Q^*\) D (elastic) D (inelastic) MR gap MR Kink

Common Mistakes to Avoid

✕ Confusing Nash with "Best"
A Nash Equilibrium is stable, not optimal. Both players may be worse off than in a cooperative outcome.
✕ Ignoring Interdependence
In oligopoly, you cannot find the profit-maximizing output without considering rival reactions. This is not perfect competition.
✕ Assuming All Games Have Dominant Strategies
Many games have no dominant strategy. You must still find Nash Equilibria by checking best responses cell by cell.

Market Structures Compared

Perfect Competition Oligopoly Monopoly
Number of Firms Many Few One
Product Type Identical Identical or differentiated Unique
Price Control None (price taker) Some (price maker) Significant
Barriers to Entry None High Very high
Interdependence None ★ High None (no rivals)
Key Tool \( MR = MC \) Game theory \( MR = MC \)

Question 1 of 5

In a Prisoner's Dilemma, the Nash Equilibrium occurs when:

Question 2 of 5

A dominant strategy is best defined as a strategy that:

Question 3 of 5

What is the Nash Equilibrium of this game, and is it collectively optimal?

Question 4 of 5

The kinked demand curve model predicts that oligopoly prices are sticky because:

Question 5 of 5

In a repeated game, which strategy best supports cooperation among oligopolists?