Équilibre dans un oligopole de Cournot

In a Cournot model, each firm chooses its production quantity by assuming its rivals' output levels remain fixed. Firms use reaction functions to determine profit-maximizing output given competitors' production decisions. This simultaneous quantity competition continues until both firms reach equilibrium, where neither has incentive to adjust output unilaterally.

A reaction curve shows the profit-maximizing production level for each firm given what competitors produce. The intersection of two firms' reaction curves represents the Cournot equilibrium, where both firms make optimal decisions. At this point, any unilateral output change by one firm reduces its profit, creating a stable market outcome.

Firms iteratively adjust production based on competitors' previous output. Firm A initially produces 50 units; Firm B responds with 25 units. Firm A then adjusts to 37.5 units, and Firm B to 31.25 units. This adjustment cycle continues until both firms produce 33.33 units each, satisfying the Nash equilibrium condition where neither firm can improve profits by changing output.

At Cournot equilibrium, both firms maximize individual profits given the rival's output level. Neither firm has incentive to unilaterally change production because doing so would reduce its profit. This stable outcome satisfies the Nash equilibrium condition, where each firm's strategy is optimal against the competitor's chosen strategy.

The Cournot model assumes firms produce homogeneous products and compete simultaneously by choosing quantities. Each firm assumes competitors' output remains fixed when making decisions. Firms act independently without collusion, and each maximizes profit based on anticipated rival behavior, creating a framework for understanding strategic decision-making in oligopolistic markets.

In monopoly, a single firm produces 50 units where marginal cost equals marginal revenue, maximizing profit without competition. In Cournot equilibrium with two firms, each produces 33.33 units, totaling 66.66 units. The competitive output exceeds monopoly output, resulting in lower market prices and reduced individual firm profits compared to monopoly conditions.

No. At Cournot equilibrium, any firm attempting to increase output to boost profit would face lower market prices, ultimately reducing its profit. Similarly, reducing output allows competitors to capture market share. The equilibrium represents a stable balance where both firms maximize profits given each other's output, preventing profitable unilateral deviations.