Core Concepts & Learning Goals
This chapter introduces oligopoly, a market structure defined by a small number of interdependent firms. Unlike firms in perfect or monopolistic competition, an oligopolist's decisions on price and quantity significantly impact its rivals, forcing it to anticipate and react to their actions. This strategic interaction is the defining feature of an oligopoly.
To understand this interdependence, we use game theory, the study of how people and firms behave in strategic situations. The "big idea" is that in an oligopoly, firms are players in a game where the profit (payoff) of one depends not only on its own strategy but on the strategies of its competitors.
By the end of this section, you will be able to define the key components of a game, use a payoff matrix to analyze strategic choices, identify dominant strategies and Nash equilibria, and explain how these concepts model the behavior of firms in an oligopoly, including their incentives to cooperate or compete.
Key Concepts Breakdown
1. The Oligopoly Market Structure
An oligopoly is an inefficient market structure characterized by a few large firms and high barriers to entry. The most critical feature is interdependence: each firm's profit depends on the actions of the other firms in the market. A market with only two firms is a special type of oligopoly called a duopoly.
Few Firms: A small number of firms control the vast majority of the market share.
High Barriers to Entry: Significant obstacles (e.g., economies of scale, patents, high start-up costs) prevent new competitors from entering the market.
Interdependence: Firms must consider the potential reactions of their rivals when making decisions about pricing, output, or advertising.
2. The Incentive to Collude
Because there are only a few firms, they have a strong incentive to engage in collusion, which is an agreement among firms to coordinate their actions, often to fix prices or limit output. When firms successfully collude, they can act like a single monopolist, reducing market quantity, raising the price, and earning higher collective profits.
A formal organization of producers that agrees to coordinate prices and production is called a cartel. While cartels are profitable for the firms involved, they are illegal in many countries because they harm consumers. More importantly, even when possible, cartels are inherently unstable because each individual firm has an incentive to cheat on the agreement.
3. Introduction to Game Theory
Game theory provides the tools to analyze strategic interdependence.
A game is any situation where the outcome for a participant (their payoff) depends on the actions of all participants (players).
A player is a participant in the game who makes a strategic decision.
A strategy is a complete plan of action a player will take in a game.
The payoff is the outcome (e.g., profit for a firm, jail time for a prisoner) that a player receives from a particular combination of strategies.
These elements are typically organized in a payoff matrix, a table that shows the payoffs for each player for every possible combination of strategies. This is also known as the normal form model of a game.
4. Dominant Strategies
A player has a dominant strategy when one of their available actions yields a higher payoff than any other action, no matter what the other player does. It is the best choice for that player, regardless of the opponent's strategy.
To find a dominant strategy for a player, you must compare their payoffs for each of their choices, holding the other player's strategy constant. If one choice is consistently better, it is a dominant strategy. A game may have one player with a dominant strategy, both players with a dominant strategy, or neither player with a dominant strategy.
5. Nash Equilibrium
A Nash equilibrium is a set of strategies, one for each player, where no player can improve their payoff by unilaterally changing their own strategy. In other words, given the choice of the other player, each player is happy with their choice and has no incentive to move.
To find a Nash equilibrium in a payoff matrix:
For each choice the column player can make, determine the best response for the row player and mark that payoff.
For each choice the row player can make, determine the best response for the column player and mark that payoff.
Any cell in the matrix where both payoffs are marked is a Nash equilibrium.
A game can have one Nash equilibrium, multiple Nash equilibria, or no Nash equilibrium in pure strategies. If both players have a dominant strategy, the outcome where both play their dominant strategies is always a Nash equilibrium.
6. The Prisoner's Dilemma and Oligopoly Behavior
The "Prisoner's Dilemma" is a famous game that illustrates why cooperation is difficult to maintain, even when it is mutually beneficial. The story involves two prisoners who, by pursuing their own self-interest, end up with a worse outcome than if they had cooperated.
This is a powerful analogy for oligopolies.
Cooperative Outcome: Firms could collude to charge a high price and earn monopoly profits (the best collective outcome).
Incentive to Cheat: Each firm has an individual incentive to break the agreement and lower its price to capture more market share and a temporarily higher profit.
Non-Cooperative Equilibrium: When both firms act on their incentive to cheat, they both end up charging a lower price and earning less profit than they would have if they had cooperated. This is a Nash equilibrium.
Because of this dilemma, oligopolies often fail to achieve the monopoly outcome. The resulting market equilibrium is inefficient, with prices generally higher and quantities lower than in perfect competition, but with prices lower and quantities higher than in a monopoly.
Payoff Matrix Analysis (Text-Only)
A payoff matrix is the primary tool for analyzing a simple game. Let's consider a duopoly where two firms, Firm A and Firm B, must decide whether to set a High Price or a Low Price. The profits (payoffs) are shown in the matrix below. The convention is that the first number in each cell is the payoff for the Row Player (Firm A) and the second number is for the Column Player (Firm B).
Payoff Matrix: High/Low Pricing Game
| Firm B Strategy | ||
|---|---|---|
| High Price | Low Price | |
| Firm A Strategy | ||
| High Price | ($100, $100) | ($20, $120) |
| Low Price | ($120, $20) | ($50, $50) |
How to Read the Matrix:
If Firm A chooses "High Price" and Firm B chooses "High Price," Firm A gets $100 and Firm B gets $100.
If Firm A chooses "Low Price" and Firm B chooses "High Price," Firm A gets $120 and Firm B gets $20.
Finding a Dominant Strategy for Firm A (Row Player):
Assume Firm B chooses "High Price." Firm A can choose "High Price" (payoff $100) or "Low Price" (payoff $120). Firm A prefers "Low Price."
Assume Firm B chooses "Low Price." Firm A can choose "High Price" (payoff $20) or "Low Price" (payoff $50). Firm A prefers "Low Price."
Because "Low Price" is the best strategy for Firm A regardless of Firm B's choice, it is Firm A's dominant strategy.
Finding a Nash Equilibrium:
From Firm A's perspective: If B plays High, A's best move is Low ($120 > $100). If B plays Low, A's best move is Low ($50 > $20).
From Firm B's perspective: If A plays High, B's best move is Low ($120 > $100). If A plays Low, B's best move is Low ($50 > $20).
Both players have a dominant strategy to play "Low Price." The outcome where both play their dominant strategy is the cell (Low Price, Low Price). This is the Nash Equilibrium. In this equilibrium, both firms earn $50. Notice that this outcome is worse for both firms than the cooperative outcome of (High Price, High Price), where they would each earn $100.
Step-by-Step Example
Let's analyze a new game between two airlines, AirLift and FlyRight, deciding on their advertising budgets. They can choose either a "High Budget" or a "Low Budget."
Payoff Matrix: Advertising Game
| FlyRight Strategy | ||
|---|---|---|
| High Budget | Low Budget | |
| AirLift Strategy | ||
| High Budget | ($60, $60) | ($90, $40) |
| Low Budget | ($40, $90) | ($80, $80) |
Step 1: Identify Players, Strategies, and Payoffs
Players: AirLift (Row) and FlyRight (Column).
Strategies: High Budget or Low Budget for each player.
Payoffs: The profits in millions of dollars, with AirLift's payoff listed first in each cell.
Step 2: Determine Dominant Strategies
AirLift's perspective:
If FlyRight chooses "High Budget," AirLift's best move is "High Budget" ($60 > $40).
If FlyRight chooses "Low Budget," AirLift's best move is "High Budget" ($90 > $80).
Therefore, AirLift has a dominant strategy: choose "High Budget."
FlyRight's perspective:
If AirLift chooses "High Budget," FlyRight's best move is "High Budget" ($60 > $40).
If AirLift chooses "Low Budget," FlyRight's best move is "High Budget" ($90 > $80).
Therefore, FlyRight also has a dominant strategy: choose "High Budget."
Step 3: Find the Nash Equilibrium
Since both players have a dominant strategy, the Nash equilibrium is the outcome where both play that strategy. The equilibrium is (High Budget, High Budget), where both firms earn a profit of $60 million.
Step 4: Calculate an Incentive to Alter a Strategy
Suppose the government wants to encourage airlines to spend less on advertising and offers a subsidy to FlyRight to change its behavior. How large must the subsidy be to make "Low Budget" a dominant strategy for FlyRight?
We need FlyRight's payoff for "Low Budget" to be higher than its payoff for "High Budget," regardless of what AirLift does.
Case 1: AirLift chooses High Budget. FlyRight's payoff for High is $60 and for Low is $40. To make Low better, the subsidy (S) must satisfy: $40 + S > $60, which means S > $20.
Case 2: AirLift chooses Low Budget. FlyRight's payoff for High is $90 and for Low is $80. To make Low better, the subsidy (S) must satisfy: $80 + S > $90, which means S > $10.
To make "Low Budget" a dominant strategy, the incentive must be sufficient in the tougher case (Case 1). Therefore, the subsidy must be greater than $20 million. Any incentive sufficient to alter a player's dominant strategy must be large enough to change the choice that provides the biggest temptation to stick with the original strategy.
AP Exam Tips & Common Pitfalls
[FRQ Task]: Be prepared to analyze a payoff matrix. You will need to identify dominant strategies, find the Nash equilibrium, and explain why players have an incentive to collude or to cheat on a collusive agreement.
[MCQ Task]: Expect questions that require you to quickly find the Nash equilibrium in a 2x2 payoff matrix or identify the dominant strategy for one or both players.
[Common Pitfall ①]: Reading the Payoff Matrix. Always remember which number in the cell belongs to which player. A common convention is (Row Player, Column Player). Before starting, confirm how the payoffs are assigned. Misreading the payoffs leads to incorrect conclusions about strategies and equilibria.
[Common Pitfall ②]: Dominant Strategy vs. Nash Equilibrium. A dominant strategy is a strategy (a single action, like "Low Price"), while a Nash equilibrium is an outcome (a specific cell in the matrix resulting from a set of strategies, like (Low Price, Low Price)). Not every game has a dominant strategy for every player, but every simple game in this course will have at least one Nash equilibrium.
Key Vocabulary
Oligopoly: A market structure with a few large, interdependent firms and high barriers to entry.
Game Theory: The study of strategic decision-making where an individual's success in making choices depends on the choices of others.
Payoff Matrix: A table showing the payoffs (e.g., profits) for every possible combination of strategies chosen by the players in a game.
Dominant Strategy: A strategy that yields the highest payoff for a player regardless of the other player's actions.
Nash Equilibrium: An outcome in a game where no player can benefit by unilaterally changing their strategy, given the strategies of the other players.