Oligopoly and Game Theory: Structured Study Notes

Oligopoly and Game Theory

Overview of Oligopoly Markets

An oligopoly is a market structure characterized by a small number of firms whose decisions are interdependent. Strategic decision-making is central, as each firm's actions affect the others.

• Few competitors: Markets with only a handful of firms.

• Strategic decision-making: Firms must consider rivals' potential responses when making choices.

• Game Theory: The study of strategic interactions among rational decision-makers.

Example: The automobile industry, where a few major companies dominate and must anticipate competitors' pricing and production decisions.

Market Structure Spectrum

Oligopoly lies between monopolistic competition and monopoly on the spectrum of market structures.

• Monopolistic Competition: Many firms, differentiated products, limited price control.

• Oligopoly: Few firms, significant price control, strategic interaction.

• Monopoly: One firm, complete price control.

Additional info: Oligopolies often exhibit higher prices and lower output than perfectly competitive markets, but less than monopolies.

Studying Oligopoly Behavior

Complexity of Oligopoly Analysis

Analyzing oligopoly behavior is complicated because firms are mutually interdependent, unlike in perfect competition or monopoly.

• Interdependence: Profits of one firm depend on the actions of other firms.

• Strategic Decision-Making: Firms must anticipate and react to competitors' moves.

Example: If one airline lowers its fares, others may follow, affecting all firms' profits.

Cartels in Oligopoly

Definition and Characteristics of Cartels

A cartel is a group of firms that collude to act as a monopoly, setting prices and output to maximize joint profits.

• Undifferentiated product: Cartels often form in markets with standardized goods.

• Small number of producers: Easier to coordinate and enforce agreements.

• Textbook example: OPEC (Organization of Petroleum Exporting Countries) in the oil market.

Cartel Formation and Output Quotas

Cartel members agree to restrict output to the monopoly level and divide production among themselves.

• Step 1: Set total output at the monopoly quantity ($Q_M$) where joint profits are maximized.

• Step 2: Assign a production quota to each member: $\text{Quota} = Q_M / n$ (where $n$ is the number of firms).

Example: If $Q_M = 48$ and there are 4 firms, each firm produces $12$ units.

Competitive vs. Cartel Outcomes

Cartels aim to move the market from competitive equilibrium to monopoly-like outcomes.

• Competitive market: $Q_C = 100$, price is lower, profits are minimal.

• Cartel: $Q_M = 48$, price is higher, profits ($\pi$) are maximized and shared.

Graphical Representation: Cartel restricts output, raising price and creating monopoly profit area ($\pi$).

Cheating in Cartels

Individual firms have incentives to cheat by producing more than their quota, increasing their own profit but destabilizing the cartel.

• Cheating increases individual output: Firm 1 produces 24 units instead of 12.

• Market price falls: Cheating increases total supply, lowering price for all.

• Profit redistribution: Cheater gains more profit, others lose.

Example: If Firm 1 cheats, it benefits from higher sales, but the overall cartel profit decreases.

Mathematical Formulation

Monopoly and Cartel Output

• Monopoly profit maximization: Set $MR = MC$ to find $Q_M$.

• Cartel quota per firm: $\text{Quota} = Q_M / n$

Example Calculation: If $Q_M = 48$ and $n = 4$, then $\text{Quota} = 12$ units per firm.

Summary Table: Competitive vs. Cartel Outcomes

Market Structure	Total Output ($Q$)	Price ($P$)	Profit ($\pi$)
Competitive	100	Low	Minimal
Cartel/Monopoly	48	High	Maximized, shared among firms

Key Terms and Concepts

• Oligopoly: Market with a small number of firms, high barriers to entry, and strategic interaction.

• Cartel: Group of firms colluding to act as a monopoly.

• Quota: Production limit assigned to each cartel member.

• Cheating: When a cartel member produces more than its quota, undermining the cartel.

• Strategic Decision-Making: Considering rivals' actions when making choices.

Conclusion

Oligopoly markets are defined by strategic interactions among a few firms. Cartels are a form of collusion that can move the market toward monopoly outcomes, but they are inherently unstable due to incentives to cheat. Understanding these dynamics is essential for analyzing real-world industries such as oil, airlines, and pharmaceuticals.