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Cournot Competition: Quantity Competition in Oligopoly

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Game Theory BasicsOligopoly and Strategic Behavior+3 more→→Bertrand Competition: Price Competition in OligopolyCartels and Collusion: Cooperation in Oligopoly+2 more
industrial-organization oligopoly

Core Idea

Firms simultaneously choose quantities of a homogeneous product; price clears the market. Each firm's profit depends on its output and rivals' outputs. Cournot-Nash equilibrium occurs where each firm optimizes given rivals' quantities. As competitors increase, equilibrium price approaches marginal cost. Cournot yields prices between monopoly and perfect competition.

Explainer

From oligopoly theory, you know that a small number of firms interact strategically — each firm's optimal decision depends on what rivals do. Cournot competition gives this intuition its first precise mathematical formulation. The setup is clean: two or more firms produce an identical product, each simultaneously chooses how much to produce, and the market price is determined by total industry output through a downward-sloping demand curve. Each firm's profit equals price times its own quantity minus its costs — but since price depends on everyone's combined output, each firm must anticipate what rivals will produce.

The key analytical tool is the best-response function (also called the reaction function). For each possible quantity that firm 2 might produce, firm 1 calculates its profit-maximizing quantity by setting marginal revenue equal to marginal cost — the same profit-maximization logic from basic microeconomics, except that marginal revenue now depends on the rival's output. With linear demand and constant marginal costs, the best-response function is a downward-sloping line: when firm 2 produces more, the residual demand facing firm 1 shrinks, so firm 1 optimally produces less. Firm 2's best-response function is symmetric. The Cournot-Nash equilibrium is the intersection of these two reaction functions — the pair of quantities where each firm is best-responding to the other, and neither wants to change.

Consider a concrete example. Suppose market demand is P = 100 − Q (where Q is total quantity), both firms have marginal cost of 10, and there are no fixed costs. A monopolist would produce 45 units at a price of 55, earning profit of 2,025. In the Cournot duopoly, each firm produces 30 units (total 60), price falls to 40, and each earns profit of 900 — industry profit is 1,800, less than the monopoly profit of 2,025. The competitive outcome would be Q = 90, P = 10, with zero profit. Cournot sits between these extremes. Each firm restricts output relative to the competitive level (earning positive profit) but produces more than the joint-monopoly quantity (because each firm ignores the negative externality its output imposes on the rival's revenue).

This framework scales naturally. With N identical firms, each produces less individually but the industry produces more in total. As N grows, the Cournot equilibrium converges smoothly to the perfectly competitive outcome — price approaches marginal cost and individual market shares shrink toward zero. This convergence result is powerful: it shows perfect competition as the limiting case of oligopoly rather than a separate model. Cournot competition also provides the foundation for richer models: Stackelberg competition adds sequential timing, Bertrand competition switches the strategic variable to prices, and collusion models ask whether firms can sustain the joint monopoly outcome through repeated interaction.

Practice Questions 5 questions

Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Number Bonds to 10 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Literal Equations → Slope-Intercept Form → Point-Slope Form → Writing Linear Equations → Parallel and Perpendicular Line Slopes → Graphing Linear Equations → Piecewise Functions → One-Sided Limits → Continuity Definition → Limits and Continuity in Multiple Variables → Functions of Several Variables → Continuity in Multiple Variables → Partial Derivatives: Definition and Computation → Differentiability in Multiple Variables → Differentiability in Multivariable Functions → Total Differential and Linear Approximation → Chain Rule for Multivariable Functions → Implicit Differentiation → Related Rates → Optimization Problems → Critical Points of Multivariable Functions → Critical Points and Classification of Extrema → Second Partial Test for Local Extrema (Hessian) → The Hessian Matrix and Second Derivative Test → Unconstrained Optimization: Finding Extrema → Optimization in Multiple Variables → Lagrange Multipliers → Constrained Optimization and Lagrange Multipliers → Utility and Preferences → Marginal Utility and Diminishing Returns → Profit Maximization → Perfect Competition → Shutdown and Breakeven Decisions → Monopoly → Monopolistic Competition → Oligopoly and Strategic Behavior → Game Theory Basics → Cournot Competition: Quantity Competition in Oligopoly

Longest path: 99 steps · 522 total prerequisite topics

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