AP MICROECONOMICS • IMPERFECT COMPETITION

Oligopoly and Game Theory

Understanding how a few dominant firms strategically interact to shape prices, output, and market outcomes.

Historical Context & Motivation

Classical economics long divided markets into two neat categories: perfect competition, with many small firms, and monopoly, with a single dominant seller. Yet most real-world industries—airlines, automobiles, wireless telecommunications, oil production—fit neither extreme. In these markets, a handful of large firms watch each other's every move, and the profit of each depends critically on the decisions of its rivals. This interdependence is the defining feature of oligopoly, and economists needed an entirely new toolkit to analyze it.

1838
Cournot's Duopoly Model
French mathematician Augustin Cournot published the first formal model of duopoly, showing how two firms choosing quantities simultaneously reach a predictable equilibrium between monopoly and competitive output levels.
1883
Bertrand's Price Competition
Joseph Bertrand challenged Cournot by arguing that firms compete on price rather than quantity. His model demonstrated that even two firms can drive price down to marginal cost under certain conditions—a strikingly different prediction.
1944
Von Neumann & Morgenstern
John von Neumann and Oskar Morgenstern published Theory of Games and Economic Behavior, establishing game theory as a rigorous mathematical framework for analyzing strategic interaction among rational agents.
1950
Nash Equilibrium
John Nash proved the existence of equilibrium in non-cooperative games, giving economists a universal solution concept: a set of strategies where no player can improve their payoff by unilaterally changing their choice.
1994
Nobel Prize for Game Theory
Nash, Harsanyi, and Selten received the Nobel Memorial Prize in Economics, confirming game theory's central role in modern economic analysis of oligopoly, bargaining, and auctions.

The central question that oligopoly theory addresses is this: when only a few firms dominate a market, how do they set prices and quantities, and why do outcomes tend to fall between the extremes of perfect competition and monopoly? Because each firm's optimal decision depends on what its rivals do, standard supply-and-demand analysis breaks down. Game theory provides the logical framework to resolve this interdependence, and it is a core component of the AP Microeconomics exam.

Core Principles & Definitions

An oligopoly is a market structure in which a small number of firms account for the dominant share of industry output. Products may be homogeneous (like steel or crude oil) or differentiated (like smartphones or automobiles). The essential characteristic distinguishing oligopoly from other structures is mutual interdependence: each firm must consider how its rivals will react before making pricing or output decisions. High barriers to entry—economies of scale, patents, large capital requirements—keep the number of firms small and protect above-normal profits over time.

1

Mutual Interdependence

Each firm's profit depends not only on its own price and quantity decisions but also on the strategies chosen by its rivals. This is what makes oligopoly fundamentally different from monopolistic competition or perfect competition.
2

Barriers to Entry

Significant obstacles—economies of scale, control of key resources, patents, or large startup costs—prevent new firms from entering the market, preserving the small number of competitors and enabling long-run economic profits.
3

Dominant Strategy & Nash Equilibrium

A dominant strategy yields the highest payoff regardless of rivals' choices. A Nash equilibrium is a strategy profile where no firm can unilaterally improve its payoff—the core solution concept for analyzing oligopoly outcomes.
4

Collusion vs. Competition

Firms have a collective incentive to collude (restrict output, raise prices) but an individual incentive to cheat on agreements. This tension between cooperation and defection is captured by the prisoner's dilemma framework.
5

The Kinked Demand Curve

This model explains price rigidity in oligopoly: rivals match price cuts (making demand inelastic below the kink) but ignore price increases (making demand elastic above the kink), creating a discontinuity in the marginal revenue curve.
KEY TAKEAWAY
Think of an oligopoly like a poker table with only four players. In a crowded tournament (perfect competition), your individual bets barely affect the pot. At a four-person table, every bet, bluff, and fold directly shapes what your opponents do next. Your optimal strategy depends on reading the other players—just as an oligopolist's pricing decision depends on anticipating rival reactions. Game theory is the playbook for this strategic poker game.

The Prisoner's Dilemma Payoff Matrix

The prisoner's dilemma is the foundational game-theory model for understanding why oligopolistic firms often fail to maintain collusive agreements. Two firms must independently choose between a cooperative strategy (keeping output low and prices high) and a competitive strategy (increasing output or cutting price to steal market share). The payoff matrix below shows profits (in millions) for each combination of strategies.

The payoff matrix illustrates the prisoner's dilemma facing two oligopolistic firms. The Nash equilibrium occurs in the lower-right cell (both cheat, earning $8M each), even though both firms would prefer the upper-left cell (both collude, earning $12M each). Cheating is each firm's dominant strategy because it yields a higher payoff regardless of the rival's choice: $18M vs. $12M if the rival colludes, and $8M vs. $4M if the rival cheats.

Notice the tension at the heart of the matrix. Collectively, the firms maximize joint profit by colluding ($12M + $12M = $24M), but individually each firm can gain by cheating ($18M > $12M). When both follow their dominant strategy and cheat, they end up at the Nash equilibrium ($8M + $8M = $16M)—a worse collective outcome than collusion, yet one from which neither has an incentive to deviate unilaterally. This is precisely why cartels, such as OPEC, persistently face instability: the temptation to produce above the agreed quota is built into the payoff structure.

Mathematical Framework

The Cournot Duopoly Model

In the Cournot model, two firms simultaneously choose quantities. Market price is determined by the inverse demand function, and each firm's profit depends on both its own output and its rival's output. Although the AP exam does not require full derivations, understanding the logic of the Cournot equilibrium deepens your grasp of oligopoly behavior and Nash equilibrium.

INVERSE MARKET DEMAND
P = a − b(Q₁ + Q₂)
P = market price; a = demand intercept; b = slope parameter; Q1 and Q2 = output of Firm 1 and Firm 2 respectively.
FIRM 1 PROFIT FUNCTION
π₁ = P × Q₁ − TC₁ = [a − b(Q₁ + Q₂)] × Q₁ − c × Q₁
π1 = Firm 1's profit; c = constant marginal cost (assuming identical firms with MC = c and no fixed costs).
BEST RESPONSE FUNCTION (REACTION FUNCTION)
Q₁* = (a − c) / (2b) − Q₂ / 2
Derived by taking ∂π1/∂Q1 = 0 and solving for Q1. Each firm's optimal quantity is a decreasing function of the rival's output.
COURNOT–NASH EQUILIBRIUM OUTPUT
Q₁* = Q₂* = (a − c) / (3b)
Solving the two reaction functions simultaneously (by symmetry) yields each firm's equilibrium output. Total market output Q = 2(a − c)/(3b) lies between the monopoly output (a − c)/(2b) and the competitive output (a − c)/b.

Key Comparisons: Output & Price by Market Structure

As the number of firms increases, Cournot output approaches the competitive outcome and price approaches marginal cost.
Market StructureTotal Output (Q)Market Price (P)
Monopoly(a − c) / (2b)(a + c) / 2
Cournot Duopoly2(a − c) / (3b)(a + 2c) / 3
Perfect Competition(a − c) / bc (= MC)
📝 AP EXAM TIP
You will not be asked to derive Cournot reaction functions on the AP exam. However, understanding the logic—that oligopoly output lies between monopoly and competitive levels, and that the Nash equilibrium occurs where reaction functions intersect—is essential for conceptual questions and FRQs on game theory outcomes.

The Kinked Demand Curve Model

While the prisoner's dilemma explains why firms struggle to maintain collusion, the kinked demand curve model explains a commonly observed feature of oligopolistic markets: price rigidity. The model rests on an asymmetric assumption about rival behavior. If one firm raises its price above the prevailing level, rivals will not follow—causing the price-raising firm to lose significant market share (demand is relatively elastic above the current price). If one firm cuts its price, rivals will match the cut to protect their market share—so the price-cutting firm gains few additional customers (demand is relatively inelastic below the current price). This asymmetry produces a kink in the demand curve at the prevailing price, and a corresponding vertical gap in the marginal revenue curve.

The kinked demand curve (cyan) has a steeper slope below the kink point (P*, Q*) because rivals match price cuts, making demand less responsive. Above the kink, demand is flatter because rivals do not match price increases. The vertical gap in the MR curve (red) means that marginal cost can shift between MC₁ (green) and MC₂ (orange) without changing the profit-maximizing price or quantity. This explains why oligopoly prices often remain sticky even when costs change.

The key implication for the AP exam is straightforward: the kinked demand model predicts that oligopoly prices will be sticky because moderate shifts in marginal cost pass through the gap in the MR curve without affecting the profit-maximizing output. Firms will maintain the prevailing price unless costs change dramatically enough to push MC above or below the gap. Note, however, that the kinked demand model has a significant limitation: it explains why prices remain rigid at the current level but does not explain how that prevailing price was determined in the first place.

Worked Example: Identifying the Nash Equilibrium

Consider two airlines, Sky Airlines and Jet Airlines, that dominate a particular route. Each must decide whether to set a high fare or a low fare. The payoff matrix below shows quarterly profits in millions of dollars (Sky's payoff listed first).

Quarterly profits (Sky, Jet) in millions
Jet: High FareJet: Low Fare
Sky: High Fare$10M , $10M$3M , $15M
Sky: Low Fare$15M , $3M$6M , $6M
Finding the Nash Equilibrium
1
Step 1 — Identify Sky Airlines' best response to each of Jet's strategiesIf Jet sets a high fare, Sky earns $10M with a high fare and $15M with a low fare → Sky's best response is low fare. If Jet sets a low fare, Sky earns $3M with a high fare and $6M with a low fare → Sky's best response is again low fare.
Low fare is Sky's dominant strategy.
2
Step 2 — Identify Jet Airlines' best response to each of Sky's strategiesIf Sky sets a high fare, Jet earns $10M with a high fare and $15M with a low fare → Jet's best response is low fare. If Sky sets a low fare, Jet earns $3M with a high fare and $6M with a low fare → Jet's best response is again low fare.
Low fare is Jet's dominant strategy.
3
Step 3 — Identify the Nash equilibriumSince both firms have a dominant strategy of setting a low fare, the Nash equilibrium occurs where both choose low fare. At this outcome, neither firm can unilaterally switch to a high fare and improve its profit: switching from $6M to $3M would be worse.
Nash Equilibrium: (Low Fare, Low Fare) → ($6M, $6M)
4
Step 4 — Evaluate the collusive outcomeIf the two airlines could credibly commit to both charging a high fare, each would earn $10M instead of $6M. The collusive outcome (High, High) produces higher joint profit ($20M vs. $12M) but is unstable: each firm individually profits from deviating to a low fare. This is the classic prisoner's dilemma.
The collusive outcome ($10M, $10M) is not a Nash equilibrium and is therefore unstable.

Oligopoly Models: Strengths & Limitations

There is no single, universally accepted model of oligopoly—unlike perfect competition or monopoly, which have definitive models. The AP exam expects you to know several approaches and understand when each applies. The table below compares the key oligopoly models you should be familiar with.

Comparison of oligopoly models tested on the AP Microeconomics exam
ModelKey AssumptionPredictionLimitation
Game Theory / Prisoner's DilemmaFirms choose strategies simultaneously; payoffs are common knowledgeDominant strategy leads to Nash equilibrium; collusion tends to break downSimple 2×2 games may oversimplify real markets with many strategies
Kinked Demand CurveRivals match price cuts but ignore price increasesPrice rigidity; output stable despite moderate cost shiftsDoes not explain how the initial equilibrium price is set
Collusion / CartelFirms cooperate to act as a joint monopolistOutput restricted, prices raised to monopoly levelCartels are illegal in the U.S.; cheating incentive makes them unstable
Price LeadershipOne dominant firm sets price; smaller firms followTacit coordination without explicit agreementLeader's power depends on cost advantage; may invite antitrust scrutiny
KEY TAKEAWAY
Think of these models as different lenses for the same phenomenon, much like how physicists use Newtonian mechanics for everyday motion but switch to relativistic mechanics at high velocities. The game-theory lens is most useful when firms make one-shot or repeated strategic decisions; the kinked demand lens applies when you observe stable prices in a particular market; and the cartel/collusion lens is relevant when firms find mechanisms to coordinate. The AP exam may ask you to apply any of these depending on the scenario described.

Connections to Efficiency, Policy & Advanced Theory

Oligopoly markets generally produce outcomes that are neither allocatively nor productively efficient. Because firms have market power, price exceeds marginal cost (P > MC), meaning society underproduces the good relative to the socially optimal level. Firms may also produce at above-minimum average total cost, failing productive efficiency. Deadweight loss exists, though it is typically less than under monopoly since competition among the few exerts some downward pressure on price. Government policy responds through antitrust regulation—the Sherman Act and Clayton Act in the United States—which prohibit explicit collusion (price fixing, market allocation) and scrutinize mergers that would significantly reduce competition.

AP scope vs. advanced extensions in oligopoly and game theory
FeatureAP Microeconomics ScopeAdvanced / College Extension
Game TypeSimultaneous, one-shot games (prisoner's dilemma)Sequential games (Stackelberg leader-follower), repeated games, mixed strategies
Equilibrium ConceptNash equilibrium, dominant strategySubgame-perfect equilibrium, Bayesian Nash equilibrium
CooperationWhy cartels are unstable; basic repeated-game intuitionFolk theorem: cooperation sustainable in infinitely repeated games if discount factor is high enough
Welfare AnalysisP > MC → deadweight loss; comparison to competitive outcomeOligopoly welfare theorems, mechanism design for auctions

For the AP exam, the most important connection is between game theory and market efficiency. When you encounter an FRQ asking about oligopoly, you should be prepared to discuss the deadweight loss that results from restricted output, compare the oligopoly outcome to perfect competition and monopoly, and explain how antitrust law attempts to push markets toward more competitive outcomes. In college-level industrial organization courses, you would extend these ideas to sequential games (where one firm moves first), auction design, and the role of information asymmetry in strategic settings.

Practice Problems

1
Which of the following best explains why oligopolistic firms are described as "mutually interdependent"?
2
Two firms, Alpha and Beta, each choose between a high price and a low price. The payoff matrix shows profits (Alpha, Beta) in thousands: (High, High) = ($50, $50); (High, Low) = ($20, $60); (Low, High) = ($60, $20); (Low, Low) = ($30, $30). What is the Nash equilibrium of this game?
3
In the kinked demand curve model, an oligopolistic firm's marginal cost increases moderately. Which of the following outcomes is most likely, assuming the new MC curve still passes through the gap in the MR curve?
PROBLEM 4APPLIED
Two wireless carriers, TelcoX and TelcoY, dominate the national market for mobile service. They must independently decide whether to spend $500 million on a 5G network upgrade (Invest) or maintain their current 4G network (Not Invest). The payoff matrix below shows annual profits in billions of dollars (TelcoX, TelcoY): | | TelcoY: Invest | TelcoY: Not Invest | |---|---|---| | TelcoX: Invest | ($5B, $5B) | ($12B, $2B) | | TelcoX: Not Invest | ($2B, $12B) | ($8B, $8B) | (a) Identify the dominant strategy for each firm. Explain your reasoning. (b) Identify the Nash equilibrium of this game. (c) Is the Nash equilibrium the outcome that maximizes joint (combined) profits? Explain. (d) Explain how this game illustrates the prisoner's dilemma. (e) If this game were repeated indefinitely, explain how the outcome might differ from the one-shot Nash equilibrium. (f) Draw a correctly labeled graph showing deadweight loss in an oligopoly market compared to the perfectly competitive outcome.
PROBLEM 5CRITICAL THINKING
A market has four firms, each with 25% market share. The firms sell identical products and face identical cost structures. (a) Explain why the kinked demand curve model would predict price stability in this market. (b) Suppose the government imposes a per-unit tax on all four firms equally. Using the kinked demand curve model, explain under what conditions the tax would or would not cause the firms to raise their price. (c) Explain one reason why the kinked demand curve model may fail to predict actual firm behavior in this market.

Summary

An oligopoly is a market structure dominated by a few firms whose decisions are mutually interdependent, meaning each firm's optimal price and output depend on the strategies of its rivals. High barriers to entry maintain the small number of firms and support long-run economic profits. Game theory provides the analytical framework for this interdependence, with the prisoner's dilemma illustrating why firms with dominant strategies to cheat often end up at a Nash equilibrium that is worse for everyone than the collusive outcome.

The kinked demand curve model explains price rigidity by positing that rivals match price cuts but ignore price increases, creating a gap in the marginal revenue curve that absorbs moderate cost shifts. Oligopolies produce allocative inefficiency (P > MC) and deadweight loss, though less than a pure monopoly. Antitrust policy targets explicit collusion and anti-competitive mergers. On the AP exam, be ready to read payoff matrices, identify dominant strategies and Nash equilibria, explain why collusion is unstable, draw the kinked demand curve, and analyze oligopoly welfare effects.

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