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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.
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.