Questions: Collusion, Cartels, and Stability

Question 1

Two firms have agreed to collude at monopoly output levels. One firm is considering secretly expanding its output. Why is cheating individually rational, even though it harms the cartel?

• A. The cheating firm earns extra revenue by undercutting the agreed price while the rival still restricts output, capturing more sales at a still-high price
• B. Cheating is only rational if the rival can be permanently driven out of the market
• C. Cheating is rational only in industries with low fixed costs because margins are thin
• D. The cheating firm benefits because its rival will retaliate by also raising output, pushing price back to competitive levels

Answer: (A)

If one firm secretly expands output while the rival adheres to the agreement, the cheater sells more units at a price that is still elevated (because the rival is still restricting). This is the prisoner's dilemma structure: taking the other's cooperation as given, defecting is privately optimal. The cheater captures more than its agreed share of a still-inflated price. This is exactly why collusion is unstable without credible enforcement — the incentive to defect exists even when cooperation is jointly superior.

Question 2

A cartel has been stable for several years. Interest rates in the economy rise sharply, increasing firms' discount rates. What does this do to cartel stability?

• A. It strengthens the cartel because higher rates increase the cost of building new production capacity, protecting members' market shares
• B. It has no effect because cartel stability depends only on market concentration, not on interest rates
• C. It destabilizes the cartel because a higher discount rate reduces the present value of future collusive profits relative to the one-time cheating gain
• D. It stabilizes the cartel because firms become more risk-averse and prefer the certainty of collusive profits

Answer: (C)

The sustainability condition requires that the present value of continuing to collude (future stream of collusive profits) exceeds the one-time windfall from cheating plus the discounted stream of Cournot punishment profits. A higher discount rate reduces the present value of all future payoffs — the collusive profit stream shrinks relative to the immediate gain from defection. This is the critical economic logic: patient firms (high δ, low discount rates) can sustain collusion; impatient firms cannot. Rising interest rates are thus a genuine destabilizing force for cartels.

Question 3

In a one-shot (single-period) prisoner's dilemma game, cheating on a collusive agreement is the dominant strategy for each firm.

• T. True
• F. False

Answer: True

In a one-shot game, each firm's best response is to cheat regardless of what the other does. If the rival restricts output, cheating yields more profit. If the rival also cheats, cheating prevents being the sucker. There is no future relationship to protect, so the one-time gain from defection is unambiguously optimal. This is precisely why indefinite repetition is necessary for collusion — only the threat of future punishment creates an incentive to cooperate today.

Question 4

Cartels with more member firms are more stable than two-firm cartels because more members means better mutual monitoring of each other's output.

• T. True
• F. False

Answer: False

More firms actually destabilizes collusion, for two reasons. First, each firm's share of monopoly profits shrinks as n increases, while the temptation to cheat (proportional to the market price gap) remains large — the gain from defection is less diluted than the cooperative reward. Second, monitoring becomes harder with more participants because detecting who cheated among many firms is more difficult. The Green-Porter model formalizes this: imperfect monitoring creates uncertainty about whether a price decline reflects cheating or just demand variation, and more firms compound this problem.

Question 5

What is the grim trigger strategy, and why must the threatened punishment be credible for it to sustain collusion?

Model answer: The grim trigger strategy is: cooperate (restrict output to the agreed level) as long as all firms have cooperated in every past period; if anyone ever cheats, revert permanently to the Cournot-Nash equilibrium forever. For this to deter cheating, the threat must be credible — firms must actually follow through on the punishment. If the threatened reversion to Cournot is itself optimal once cheating occurs (it is, since Cournot is a Nash equilibrium), the threat is credible even without an external enforcer.

The credibility requirement is non-trivial. A threat to do something that would not be in your interest to actually carry out is not credible. Crucially, reverting to Cournot after cheating IS individually rational — Cournot is the static Nash equilibrium, and each firm's best response to the other playing Cournot is to play Cournot. So the punishment enforces itself. This is why grim trigger works while, say, threatening to exit the market would not — exit is too extreme and therefore not credible.