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2. USAEO Microeconomics

Oligopoly And Game Theory

Combine strategic interaction, payoff reasoning, and oligopoly outcomes in one high-yield USAEO lesson path.

Oligopoly and Game Theory

Welcome to today’s lesson on Oligopoly and Game Theory! 🎯 The goal of this lesson is to help you understand how firms in oligopolistic markets make strategic decisions and how game theory helps us predict their behavior. By the end, you’ll be able to analyze key concepts like Nash equilibria, dominant strategies, and the prisoner’s dilemma, all while connecting them to real-world economic scenarios. Ready to dive in? Let’s go!

Understanding Oligopoly: The Basics

An oligopoly is a market structure where a few large firms dominate the market. Unlike perfect competition or monopoly, oligopolies are characterized by strategic interdependence—each firm’s actions affect the others. Think of industries like airlines, telecommunications, or even the soft drink market (Coke and Pepsi, anyone?). Here are some key features:

  1. Few Sellers: Oligopolies typically have between 2 and 10 firms controlling most of the market share.
  1. Barriers to Entry: High barriers like large capital requirements, patents, or control over key inputs make it tough for new firms to enter.
  1. Interdependence: Because there are only a few firms, each one must consider the reactions of rivals when making pricing or output decisions.
  1. Non-Price Competition: Oligopolies often compete on advertising, product differentiation, and innovation rather than just on price.

Real-World Example: The Airline Industry ✈️

Imagine Delta, United, and American Airlines. These firms dominate the U.S. market. If Delta cuts ticket prices, it’s not just affecting its own customers—it’s also putting pressure on United and American to respond. This interdependence is the hallmark of an oligopoly.

Concentration Ratios and the Herfindahl-Hirschman Index (HHI)

To measure the degree of market concentration, economists use tools like the four-firm concentration ratio (CR4) and the Herfindahl-Hirschman Index (HHI).

  • CR4: This measures the total market share of the top four firms. For example, if the top four firms control 85% of the market, the CR4 is 85%.
  • HHI: This index squares the market shares of all firms and sums them up. For example, if four firms have 40%, 30%, 20%, and 10% market shares, the HHI would be:

$$

HHI = 40^2 + 30^2 + 20^2 + 10^2 = 1600 + 900 + 400 + 100 = 3000

$$

The U.S. Department of Justice considers an HHI above 2500 as a highly concentrated market.

Introduction to Game Theory: The Science of Strategy

Game theory is a powerful tool for understanding strategic interactions. It’s used in economics, political science, and even biology! At its core, game theory studies how rational decision-makers (players) choose strategies to maximize their payoffs, given the strategies of others.

Key Terms in Game Theory

  • Players: The decision-makers in the game (e.g., firms in an oligopoly).
  • Strategies: The possible actions a player can take (e.g., setting a high price or a low price).
  • Payoffs: The outcomes or rewards players receive based on the combination of strategies.
  • Dominant Strategy: A strategy that yields the highest payoff for a player, no matter what the other player does.
  • Nash Equilibrium: A situation where no player can improve their payoff by unilaterally changing their strategy. Each player’s choice is optimal, given the other players’ choices.

The Prisoner’s Dilemma: A Classic Game 🎲

Let’s start with a classic example: the prisoner’s dilemma. Two suspects (players) are arrested and interrogated separately. They can either confess (defect) or remain silent (cooperate). Here’s the payoff matrix:

| | Partner Silent (Cooperate) | Partner Confess (Defect) |

|----------------|----------------------------|--------------------------|

| You Cooperate | -1 year each | -10 years for you, 0 for them |

| You Defect | 0 years for you, -10 years for them | -5 years each |

In this game, defecting is the dominant strategy for both players. Why? Because no matter what the other player does, defecting yields a better or equal payoff. If both defect, they each get -5 years. If both cooperate, they get -1 year each. Yet, the rational outcome (both defecting) is worse for both than if they had cooperated! This illustrates the tension between individual rationality and collective outcomes.

Applying the Prisoner’s Dilemma to Oligopolies

Now let’s apply this to a real-world oligopoly. Imagine two firms, Firm A and Firm B, deciding whether to set a high price or a low price.

| | Firm B High Price | Firm B Low Price |

|----------------|-------------------|------------------|

| Firm A High Price | \$100M, \$100M | \$50M, \$120M |

| Firm A Low Price | \$120M, \$50M | \$70M, \$70M |

  • If both firms set high prices, they each earn \100M.
  • If one sets a low price while the other keeps a high price, the low-price firm earns \120M while the high-price firm earns only \50M.
  • If both set low prices, they each earn \70M.

What’s the Nash Equilibrium here? It’s for both firms to set low prices (\70M each), even though they would both be better off with high prices (\100M each). This is the oligopoly version of the prisoner’s dilemma—competition drives prices down, even if cooperation would lead to higher profits.

Types of Oligopoly Models

Economists have developed several models to explain how firms behave in oligopolies. Let’s explore three major ones: Cournot, Bertrand, and Stackelberg.

The Cournot Model: Quantity Competition

In the Cournot model, firms compete by choosing quantities. Each firm decides how much to produce, and the market price is determined by the total quantity supplied.

Example: Duopoly with Linear Demand

Let’s say there are two firms (Firm 1 and Firm 2) producing identical products. The market demand is:

$$

$P = 100 - Q$

$$

Where $P$ is the price and $Q$ is the total quantity produced ($Q = q_1 + q_2$).

Each firm has a constant marginal cost of \$20. The profit for Firm 1 is:

$$

$\pi_1$ = (P - MC) $\times$ q_1 = (100 - (q_1 + q_2) - 20) $\times$ q_1 = (80 - q_1 - q_2) $\times$ q_1

$$

To find the best response function for Firm 1, we take the derivative of $\pi_1$ with respect to $q_1$ and set it to zero:

$$

$\frac{d\pi_1}{dq_1}$ = 80 - 2q_1 - q_2 = 0

$$

So, Firm 1’s best response is:

$$

$q_1 = 40 - \frac{q_2}{2}$

$$

By symmetry, Firm 2’s best response is:

$$

$q_2 = 40 - \frac{q_1}{2}$

$$

Solving these two equations simultaneously gives the Cournot equilibrium quantities:

$$

q_1 = q_2 = $\frac{40}{1 + \frac{1}{2}}$ = $\frac{40}{1.5}$ = 26.67

$$

The total quantity $Q = 53.33$, and the price is:

$$

P = 100 - 53.33 = 46.67

$$

This is the Cournot equilibrium price and quantity. Notice how the firms split the market and the price is above marginal cost (\$20).

The Bertrand Model: Price Competition

In the Bertrand model, firms compete by setting prices instead of quantities. The key insight: if products are identical and there are no capacity constraints, the equilibrium outcome is that both firms set price equal to marginal cost.

Why? Because if one firm sets a higher price, the other firm can undercut it slightly and capture the entire market. This price-cutting continues until price equals marginal cost.

Example: Bertrand Paradox

Imagine two gas stations across the street from each other. Their marginal cost per gallon is \3. If one station sets a price of \$4, the other can set \$3.99 and get all the customers. This undercutting continues until both set the price at \$3. The surprising result: even with only two firms, the outcome is the same as perfect competition!

The Stackelberg Model: First-Mover Advantage

In the Stackelberg model, one firm moves first (the leader), and the other firm moves second (the follower). The leader commits to a quantity, and the follower observes this and then chooses its own quantity.

Example: Stackelberg Duopoly

Let’s revisit our previous Cournot example. Firm 1 is the leader, and Firm 2 is the follower. Firm 2’s best response (as we found earlier) is:

$$

$q_2 = 40 - \frac{q_1}{2}$

$$

Firm 1 knows this and maximizes its profit accordingly. Firm 1’s profit function is:

$$

$\pi_1$ = (80 - q_1 - q_2) $\times$ q_1

$$

Substituting Firm 2’s best response into this:

$$

$\pi_1$ = (80 - q_1 - (40 - $\frac{q_1}{2}$)) $\times$ q_1 = (40 - $\frac{q_1}{2}$) $\times$ q_1

$$

Taking the derivative and setting it to zero:

$$

$\frac{d\pi_1}{dq_1}$ = 40 - q_1 = 0 \implies q_1 = 40

$$

Now, Firm 2’s quantity is:

$$

q_2 = 40 - $\frac{40}{2}$ = 20

$$

So, the Stackelberg equilibrium quantities are $q_1 = 40$ and $q_2 = 20$. The total quantity is $Q = 60$, and the price is:

$$

P = 100 - 60 = 40

$$

Notice that the leader (Firm 1) produces more and earns a higher profit than the follower. This is the first-mover advantage.

Collusion and Cartels: The Temptation of Cooperation

In some oligopolies, firms try to collude—they form agreements to set prices or limit output, essentially acting like a monopoly. The most famous example is OPEC, the Organization of Petroleum Exporting Countries, which sets oil production quotas to influence global oil prices.

Why Collusion is Unstable

While collusion can yield high profits, it’s often unstable due to the incentive to cheat. If all firms agree to keep prices high, one firm can secretly lower its price to capture a larger market share. This cheating can unravel the cartel, leading to a price war.

Antitrust Laws

In many countries, collusion is illegal. In the U.S., the Sherman Antitrust Act (1890) prohibits agreements that restrain trade. Authorities like the Federal Trade Commission (FTC) monitor and punish collusive behavior to protect consumers.

Repeated Games and Cooperation

Not all games are played once. In repeated games, players interact multiple times, which can lead to cooperation. If firms know they’ll compete tomorrow, they may be less likely to undercut each other today, fearing retaliation.

Tit-for-Tat Strategy

One famous strategy in repeated games is tit-for-tat: you start by cooperating, and then you mimic whatever the other player did in the previous round. If they cooperate, you cooperate next time. If they defect, you defect. This strategy often leads to long-term cooperation, as players learn that defection is punished.

Real-World Example: Price Matching Policies

Many firms use price matching policies (“We’ll match any competitor’s price!”) as a form of tit-for-tat. This discourages price wars, because any discount by one firm will be immediately matched by others, nullifying the advantage of undercutting.

Conclusion

In this lesson, we explored the fascinating world of oligopolies and game theory. We learned how a few dominant firms interact strategically, how they make decisions based on the actions of their rivals, and how game theory helps us predict these outcomes. We examined key models like Cournot, Bertrand, and Stackelberg, and saw how concepts like the prisoner’s dilemma and Nash equilibrium apply in real-world markets. Understanding these principles is crucial for analyzing everything from airline pricing to oil production. Great job, students! Keep practicing, and soon you’ll master these essential economic tools. 🚀

Study Notes

  • Oligopoly: A market dominated by a few large firms; characterized by strategic interdependence.
  • Key Features of Oligopoly:
  • Few sellers
  • High barriers to entry
  • Interdependence of firms
  • Non-price competition
  • Concentration Ratios:
  • CR4: Total market share of the top four firms.
  • HHI: Sum of the squares of all firms’ market shares. HHI > 2500 = highly concentrated market.
  • Game Theory Terms:
  • Players: Decision-makers in the game.
  • Strategies: Possible actions each player can take.
  • Payoffs: Outcomes based on strategy combinations.
  • Dominant Strategy: Best strategy regardless of what others do.
  • Nash Equilibrium: No player can improve their payoff by changing their strategy alone.
  • Prisoner’s Dilemma:
  • Dominant strategy is often to defect.
  • Nash equilibrium is (Defect, Defect), even though (Cooperate, Cooperate) yields a better collective outcome.
  • Oligopoly Models:
  • Cournot Model: Firms compete by choosing quantities.
  • Equilibrium: Firms choose quantities based on rivals’ quantities.
  • Example: $q_1 = 40 - \frac{q_2}{2}$
  • Bertrand Model: Firms compete by setting prices.
  • Equilibrium: Price = Marginal Cost (Bertrand Paradox).
  • Stackelberg Model: One firm (leader) chooses quantity first, follower responds.
  • Leader has a first-mover advantage.
  • Example equilibrium: $q_1 = 40$, $q_2 = 20$, $P = 40$.
  • Collusion:
  • Firms may collude to set prices or limit output (e.g., OPEC).
  • Collusion is often unstable due to incentives to cheat.
  • Antitrust Laws: Prohibit collusion (e.g., Sherman Antitrust Act in the U.S.).
  • Repeated Games:
  • Repeated interactions can lead to cooperation.
  • Tit-for-Tat: Cooperate initially, then mimic the other player’s previous move.
  • Example: Price matching policies encourage cooperation.
  • Key Equations:
  • Cournot Best Response: $q_1 = \frac{a - c - q_2}{2}$ for linear demand $P = a - Q$.
  • Bertrand Equilibrium: $P = MC$ when products are identical.
  • Stackelberg Leader Quantity: Solve using follower’s best response.

Keep these notes handy, students, and use them to review the key concepts we covered today. You’re on your way to mastering oligopoly and game theory! 🌟

Practice Quiz

5 questions to test your understanding

Oligopoly And Game Theory — Olympiad USAEO Economics | A-Warded