Oligopoly: Market Structure, Game Theory, and Strategic Behavior

Oligopoly

Introduction to Oligopoly

An oligopoly is a market structure characterized by a small number of firms whose decisions are interdependent. Barriers to entry, either natural or legal, prevent new firms from entering the market, resulting in a few dominant firms that compete with one another.

• Definition: Oligopoly is a market structure in which a small number of firms compete, and natural or legal barriers prevent the entry of new firms.

• Barriers to Entry: These can be natural (e.g., economies of scale) or legal (e.g., government licensing).

• Examples: The airline industry, automobile manufacturing, and city-licensed taxi services.

Natural vs. Legal Oligopoly

• Natural Oligopoly: Occurs when economies of scale allow only a few firms to supply the market efficiently. For example, a market may support only two or three firms at minimum average cost.

• Legal Oligopoly: Exists when laws or regulations limit the number of firms, such as city licenses for taxi companies.

Comparison with Other Market Structures

• Perfect Competition: Many firms, no barriers to entry, firms are price takers, and minimum average cost is reached at a small output relative to the market.

• Monopoly: One firm, high barriers to entry, firm is a price maker, and the market is supplied by a single producer.

• Oligopoly: Few firms, significant barriers to entry, firms are interdependent, and strategic behavior is crucial.

Behavior in Oligopoly

The degree of imperfect competition in an oligopoly is influenced by both the number and size of firms and their behavior. Firms may choose between cooperative and noncooperative strategies.

• Interdependence: Each firm's profit depends on the actions of its rivals.

• Temptation to Cooperate: Firms may be tempted to form a cartel—a group of firms acting together to limit output, raise price, and increase profit. Cartels are illegal in many countries.

• Noncooperative Behavior: Firms act independently, often leading to price wars and competitive outcomes.

Cartels

• Definition: A cartel is a group of firms that collude to set prices or output to maximize joint profits.

• Example: The Organization of Petroleum Exporting Countries (OPEC) is a well-known international cartel.

• Formation: Cartels form when firms believe coordinated action will increase their profits.

Strategic Interaction and Game Theory

Oligopolistic firms engage in strategic interactions, where each firm must consider how its rivals will react to its decisions. Game theory is the primary tool used to analyze such behavior.

• Game Theory: The study of strategic behavior, where the outcome for each participant depends on the actions of all.

• Assumptions: Players aim to maximize their payoffs, and all players have common knowledge of the rules, strategies, payoffs, and outcomes.

• Common Knowledge: Information known by all players, and everyone knows that everyone knows it, and so on.

The Prisoners' Dilemma

The prisoners' dilemma is a classic example of a game that illustrates why two rational individuals might not cooperate, even if it appears that it is in their best interest to do so.

• Setup: Two prisoners (Art and Bob) are accused of a crime and held in separate cells. Each can either confess or deny the crime.

• Payoff Matrix: The outcomes depend on the combination of choices:

	Bob Confess	Bob Deny
Art Confess	3 years, 3 years	1 year (Art), 10 years (Bob)
Art Deny	10 years (Art), 1 year (Bob)	2 years, 2 years

• Nash Equilibrium: Both confessing is the Nash equilibrium, as neither can improve their outcome by changing their strategy unilaterally.

• Dilemma: The equilibrium is not the best collective outcome (both would be better off denying), but rational self-interest leads to both confessing.

Dominant Strategies

• Definition: A strategy is dominant if it yields a better outcome for a player, no matter what the other player does.

• Example: In the prisoners' dilemma, confessing is a dominant strategy for both players.

Oligopoly Price-Fixing Game (Duopoly)

In a duopoly (an oligopoly with two firms), firms may collude to maximize joint profits, but each has an incentive to cheat on the agreement.

• Collusive Agreement: Firms agree to restrict output and raise prices, acting like a monopoly.

• Profit Maximization: The cartel sets marginal cost equal to marginal revenue: $MC = MR$

• Cheating: If one firm cheats by increasing output, it can increase its profit at the expense of the other. If both cheat, the outcome is similar to perfect competition, with zero economic profit.

Payoff Matrix for Duopoly

	Gear Complies	Gear Cheats
Trick Complies	$2M, $2M	-$1M, $4.5M
Trick Cheats	$4.5M, -$1M	$0, $0

• Nash Equilibrium: Both firms cheat, resulting in zero economic profit for both.

Other Oligopoly Games

• Advertising Game: Firms may compete by advertising, which can be modeled as a prisoners' dilemma.

• R&D Game (Game of Chicken): Firms may face a situation where only one needs to invest in research and development, but both can benefit. The equilibrium is for one firm to invest, but it is uncertain which one will do so.

Summary Table: Oligopoly vs. Other Market Structures

Market Structure	Number of Firms	Barriers to Entry	Price Setting Power	Examples
Perfect Competition	Many	None	None (price taker)	Agriculture
Monopoly	One	High	High (price maker)	Utilities
Oligopoly	Few	High	Some (interdependent)	Airlines, Automobiles

Key Formulas

• Profit Maximization for Cartel: $MC = MR$

Conclusion

Oligopoly is a complex market structure where a few firms dominate and strategic behavior is essential. Game theory provides a framework for understanding the interdependence and potential outcomes, including the temptation to collude and the incentives to cheat. Real-world examples, such as OPEC and airline pricing, illustrate the practical implications of oligopoly theory.