Cartel Economics: Repeated Cournot Games and Cooperation

Cartels coordinate lower production to raise market prices. Typical examples include OPEC’s oil output limits, drug trafficking syndicates, the American Medical Association’s control of medical school enrollment, and Quebec’s government‑sponsored maple‑syrup cartel. The shared goal is to shift the market from competitive equilibrium toward a monopoly‑like outcome.

The Economic Challenge

Each member enjoys a private incentive to overproduce. When a firm raises its output, it internalizes only the profit effect on itself while imposing a negative externality on the other members by depressing the market price. Without an external court or antitrust immunity, the cartel lacks a formal enforcement mechanism, making deviation tempting.

Infinitely Repeated Cournot Competition

The lecture models the cartel as an infinitely repeated Cournot game with constant marginal cost c, an infinite horizon, and observable past actions. In the one‑shot stage game, the Nash equilibrium quantity is

[ q_{NE}= \frac{1-c}{n+1}, ]

whereas the monopoly quantity that maximizes total profit is

[ Q_M = \frac{1-c}{2}, \qquad q_M = \frac{1-c}{2n}. ]

The monopoly outcome is not a Nash equilibrium because any single firm can increase its profit by deviating to a higher quantity.

Sustaining Cooperation

Cooperation survives when firms are sufficiently patient. Let δ denote the common discount factor. The one‑shot gain from cheating is G, and the loss from future punishment is L. The equilibrium condition

[ \delta \ge \frac{G}{G+L} ]

ensures that the present value of future losses outweighs the immediate gain. High δ means firms value future profits enough to refrain from cheating.

Nash Reversion Mechanism

If any firm deviates from the agreed monopoly quantity, all firms switch forever to the stage‑game Nash equilibrium quantity. This self‑enforcing punishment eliminates any incentive to deviate once the Nash equilibrium is reached.

Automaton Representation

Analysts simplify strategy analysis by grouping histories into two states: “Monopoly” (cooperation) and “Nash” (punishment). Observed deviations trigger a transition from the Monopoly state to the Nash state, allowing the value‑function approach to compute discounted payoffs without enumerating the entire infinite path.

Advanced Punishment Strategies

Carrot‑and‑stick equilibria replace permanent reversion with a temporary “stick” phase of high production followed by a return to the “carrot” phase of low production. The length and severity of the stick phase determine L; a larger L lowers the required δ threshold. The flexibility of limited‑duration punishments can make cooperation easier to sustain when firms are less patient.

“The goal of these specific kinds of cartel is generally to coordinate on lower production in order to raise market prices.”

“When I raise my production, I only internalize the effect it has on my profits. But I'm actually hurting the other members of the cartel.”

“We don't have an external court to take you to jail if you violate it.”

“The more firms there are, the smaller this markup is.”

“If the loss gets larger, that means the punishment is very powerful… it's easier to sustain the equilibrium.”

Real‑World Illustrations of Punishment

Saudi Arabia’s “flooding the market” episode in the 1980s serves as a historical example of a stick phase: by dramatically increasing output, Saudi Arabia imposed a severe loss on other OPEC members, reinforcing the cartel’s discipline. Similar dynamics appear in drug cartels that threaten violent retaliation against members who betray the group.