AP Microeconomics: Oligopoly and Game Theory (Nash Equilibrium, Prisoner’s Dilemma, Collusion)

AP Microeconomics – Oligopoly and Game Theory (Nash Equilibrium, Prisoner’s Dilemma, Collusion)

AP Microeconomics – Oligopoly & Game Theory (Nash Equilibrium, Prisoner’s Dilemma, Collusion)

What This Is

Oligopoly is a market structure where a few large firms dominate an industry and each firm’s decisions (price, output, advertising) directly affect the others. Because firms must anticipate rivals’ reactions, they often use game?theoretic tools—most famously the Nash equilibrium and the prisoner’s?dilemma framework—to predict outcomes. Understanding these concepts is essential for the AP exam because the FRQ frequently asks you to explain why oligopolists may earn above?normal profits without explicit collusion, and to draw the kinked?demand or reaction?function graph that shows strategic interdependence.

Real?world example: The “Big?Three” U.S. airlines (American, Delta, United) decide on ticket prices and route capacity while constantly watching each other’s moves; their pricing patterns often look like a prison?er’s?dilemma—if one airline cuts fares, the others must decide whether to follow or keep prices high.

Key Terms & Formulas

• Oligopoly – A market with 2?5 large firms; each firm’s profit depends on the actions of the others.
• Game Theory – The study of strategic interaction; models decisions as “games” with defined players, strategies, and payoffs.
• Nash Equilibrium – A set of strategies where no player can improve profit by unilaterally changing its own strategy (best?response condition).
• Prisoner’s Dilemma – A two?player game where the dominant strategy (defect) leads to a worse collective outcome than mutual cooperation.
• Collusion – An explicit or tacit agreement among firms to coordinate output or price, raising industry profits above the competitive level.
• Kinked?Demand Curve – A demand curve for an oligopolist that is more elastic above the current price (rivals match price cuts) and less elastic below (rivals ignore price hikes). Axes: Price (vertical) vs. Quantity (horizontal).
• Reaction Function (Best?Response Curve) – Shows a firm’s optimal output (or price) as a function of a rival’s output (or price). Graph: Firm?A’s quantity on the vertical axis, Firm?B’s quantity on the horizontal axis; the intersection is the Nash equilibrium.
• Profit (?) = TR – TC – Total revenue minus total cost; used to compare outcomes at different equilibria.
• Cartel – A formal collusive organization (e.g., OPEC) that sets a common output or price.
• Dominant Strategy – A strategy that yields a higher payoff regardless of what rivals do.

Step?by?Step / Process Flow (Solving a Typical AP Oligopoly FRQ)

1. Identify the market structure – Look for clues: “few firms,” “price rigidity,” “mutual interdependence.”
2. Choose the appropriate game?theory model –
3. If the question mentions “price war” or “mutual price?keeping,” draw a kinked?demand graph.
4. If it asks about “strategic interaction” with explicit pay?offs, set up a payoff matrix (Prisoner’s Dilemma).
5. Label the axes and curves – For a kinked?demand graph: P on the vertical axis, Q on the horizontal; draw the kink at the current price/quantity, then sketch the marginal revenue (MR) curve with a gap (vertical distance = price rigidity).
6. Find the equilibrium –
7. In a payoff matrix, locate the Nash equilibrium (no cell where a player can improve by moving alone).
8. In a reaction?function diagram, solve the simultaneous equations of the two firms’ best?response curves; the intersection point gives each firm’s output.
9. Explain the outcome – State whether the equilibrium yields higher, lower, or the same profit as perfect competition, and discuss the role of collusion or mutual interdependence.
10. Answer the FRQ prompt – Tie the graph back to the question (e.g., “Explain why the price is sticky in this industry”) and use the appropriate terminology (Nash equilibrium, dominant strategy, etc.).

Common Mistakes

AP Exam Insights

1. Multiple?Choice Focus:
2. Questions often ask you to identify the shape of the demand curve (kinked vs. straight) given a description of price rigidity.

3. You may need to choose the correct payoff matrix for a Prisoner’s Dilemma scenario (look for “dominant strategy” language).

4. Free?Response Emphasis:

5. FRQ Part A may require you to draw a kinked?demand graph and label the MR gap, then explain why the market price is “sticky.”

6. FRQ Part B often asks you to determine the Nash equilibrium in a simple 2?firm Cournot quantity game; you’ll solve simultaneous best?response equations and compute each firm’s profit (? = (P?MC)·Q).

7. Tricky Distinctions:

8. Collusion vs. Oligopoly: Collusion is a choice (explicit or tacit); oligopoly is a structure that allows collusion.

9. Dominant Strategy vs. Nash Equilibrium: A dominant strategy leads to a Nash equilibrium, but not every Nash equilibrium involves a dominant strategy.

10. Graphing Requirements:

11. Label every axis (price, quantity, cost).
12. Mark the kink and draw the MR gap clearly.
13. For reaction functions, write the equations (e.g., Q_A = 120 – 0.5Q_B) and show the intersection point.

Quick Check Questions

1. MC: In a duopoly where each firm’s marginal cost is $10 and the market demand is P = 100 – 2Q, the firms choose quantities simultaneously (Cournot). What is the Nash?equilibrium quantity for each firm?
2. Answer: 20 units each.

3. Explanation: Best?response functions: Q_A = (90 – Q_B)/2-solving simultaneously gives Q_A = Q_B = 20.

4. FRQ?style: “The airline industry often exhibits price rigidity. Explain, using a graph, why a firm in an oligopoly might keep its price unchanged after a rival cuts fares.”

5. Answer: Draw a kinked?demand curve; the MR curve has a vertical gap. Because the MR gap makes the marginal profit unchanged for a small price increase, the firm’s optimal price stays at the kink, producing price rigidity.

6. MC: In a Prisoner’s Dilemma payoff matrix, both players have a dominant strategy to defect. Which of the following statements is true?

7. A) The outcome is Pareto?optimal.
8. B) Each player would be better off if they both cooperated.
9. C) Defecting yields a lower payoff than cooperating.
10. Answer: B) Each player would be better off if they both cooperated.
11. Explanation: Mutual cooperation gives higher payoffs than mutual defection, but rational players choose defection because it dominates.

Last?Minute Cram Sheet (10 One?Liners)

1. Oligopoly = few firms + interdependence.
2. Kinked?Demand: Elastic above kink (rivals match cuts)-MR gap-price stickiness.
3. Nash Equilibrium: No unilateral profit?improving deviation; may be inefficient.
4. Prisoner’s Dilemma: Dominant strategy = defect; equilibrium = (defect, defect).
5. Reaction Function: Q_A = a – b·Q_B (vertical axis = Firm?A’s output).
6. Profit Formula:-= (P – MC)·Q. Use it to compare outcomes at different equilibria.
7. Collusion: Explicit (cartel) = illegal; tacit = parallel behavior, not illegal.
8. Dominant Strategy: Best response regardless of opponent’s move.
9. MR Gap: Distance between MR curves above and below the kink; indicates price rigidity.
10. “Shift” vs. “Move”: A change in price moves along the demand curve; a shift (right/left) changes the curve itself.

Good luck—remember to draw the graph first, label every line, and then explain the strategic logic! ?