A Failed Cartel: When Collusive Firms Become Competitors

Source abstract

Collusion is inherently unstable because individual firms have incentives to deviate from cooperative agreements. We study a novel hybrid oligopoly market structure, termed a failed cartel, in which one firm abandons a cartel agreement while the remaining firms continue to coordinate their production decisions. We further reinterpret the Cournot–Stackelberg hybrid structure as a natural punitive benchmark following cartel breakdown, in which the remaining firms abandon cooperation and compete while facing the deviating firm as a common Stackelberg follower. From a game-theoretic perspective, each firm’s quantity choice depends on its own action, its rivals’ actions, and the resulting market state. While simple inverse demand and cost functions permit equilibrium analysis by classical profit maximization, nonlinear specifications used in oligopoly research, such as isoelastic inverse demand, generally do not yield explicit reaction functions or closed-form equilibria. We therefore represent strategic adjustment as an iterative game generated by firms’ reaction mappings: at each stage, firms revise their production quantities in response to the current market configuration. Tripled fixed points of the resulting mapping characterize equilibrium and provide conditions for existence, uniqueness, stability, and convergence of successive quantity adjustments. Numerical comparisons, ranging from an illustrative triopoly to the asymptotic regime with many firms, characterize how the failed-cartel and punitive Cournot–Stackelberg structures differ from classical markets in terms of output, prices, profits, consumer surplus, and total welfare.