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Collusion, Cartels, and Stability

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Cournot Competition: Quantity Competition in OligopolyNash Equilibrium+1 moreStackelberg Competition: Sequential Quantity Leadership
industrial-organization collusion repeated-games

Core Idea

Cartels are agreements among competitors to restrict output and elevate price toward monopoly levels, sharing monopoly profit. Collusion is unstable because each firm has incentive to cheat by undercutting the agreed price. Sustainability requires credible punishment (grim trigger: permanent reversion to Cournot) and sufficient future profit weight, with higher discount rates destabilizing collusion.

Explainer

From Cournot competition, you know that oligopolists who independently choose quantities end up at a Nash equilibrium where industry profits are lower than monopoly profits — competition dissipates some of the surplus. This creates an obvious temptation: what if firms agree to collectively restrict output to the monopoly level and split the larger pie? This is the logic behind cartels, and it immediately raises the central question of this topic: why don't all oligopolists collude, and why do cartels so often fall apart?

The instability comes directly from the structure of the Cournot game. Suppose two firms agree to each produce half the monopoly quantity. At this restricted output, the market price is high. But each firm, taking the other's restricted output as given, finds it profitable to cheat — to secretly produce more than its agreed share. The cheating firm captures extra sales at a still-high price (since the other firm is still restricting output), earning more than its share of monopoly profits. This is the same logic as the prisoner's dilemma: mutual cooperation (collusion) is jointly optimal, but individual defection is privately optimal. In a one-shot game, cheating is the dominant strategy and collusion unravels.

The resolution lies in repeated interaction. If firms compete period after period indefinitely, they can sustain collusion using trigger strategies: cooperate as long as everyone cooperates, but if anyone cheats, revert permanently to the Cournot-Nash equilibrium (the grim trigger). The cheater gains a one-period windfall from extra output but loses the stream of future collusive profits, receiving only Cournot profits forever after. Whether collusion holds depends on the discount factor (δ). The critical condition is that the present value of continued collusive profits must exceed the one-time cheating gain plus the discounted stream of punishment profits. This yields a minimum discount factor below which collusion is unsustainable — impatient firms (high discount rates, low δ) cannot maintain cartels because the immediate temptation outweighs distant future losses.

Several real-world factors map onto this framework. More firms make collusion harder — each firm's share of monopoly profit shrinks while the temptation to cheat remains large. Demand fluctuations create problems because firms cannot easily distinguish a rival's cheating from a genuine demand decline (the Green-Porter model of imperfect monitoring). Asymmetric costs make agreement on output shares contentious. Antitrust enforcement raises the cost of collusion by adding legal penalties. OPEC illustrates every element: members periodically agree to output quotas, individual members regularly exceed them, and the cartel's effectiveness varies with how patient members are and how well they can monitor each other's production.

Practice Questions 5 questions

Prerequisite Chain

Understanding ZeroThe Number ZeroCounting to FiveCounting to 10Counting to 20Counting a Set of Objects Up to 20Cardinality: The Last Number CountedMatching Numerals to QuantitiesSubitizing Small QuantitiesAddition Within 10Number Bonds to 10Addition Within 20Doubles and Near DoublesDoubles Facts Within 10Near Doubles Facts Within 20Mental Math Strategies for AdditionMental Math: Adding and Subtracting TensAddition Within 100Repeated Addition as MultiplicationMultiplication as Equal GroupsMultiplication: ArraysBasic Multiplication Facts (0s, 1s, 2s, 5s, 10s)Multiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Multiplication and Division Fact FamiliesRelationship Between Multiplication and DivisionDivision Facts as Inverse of MultiplicationRemainders and Quotients in DivisionDivision Word ProblemsMulti-Step Word ProblemsSolving Multi-Step Word ProblemsMultiplication Word ProblemsDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueIntegers and the Number LineComparing and Ordering IntegersAbsolute ValueAdding IntegersSubtracting IntegersMultiplying IntegersDividing IntegersUnit RatesProportionsPercent ConceptConverting Between Fractions, Decimals, and PercentsOperations with Rational NumbersTwo-Step EquationsSolving Multi-Step EquationsEquations with Variables on Both SidesLiteral EquationsSlope-Intercept FormPoint-Slope FormWriting Linear EquationsParallel and Perpendicular Line SlopesGraphing Linear EquationsPiecewise FunctionsOne-Sided LimitsContinuity DefinitionLimits and Continuity in Multiple VariablesFunctions of Several VariablesContinuity in Multiple VariablesPartial Derivatives: Definition and ComputationDifferentiability in Multiple VariablesDifferentiability in Multivariable FunctionsTotal Differential and Linear ApproximationChain Rule for Multivariable FunctionsImplicit DifferentiationRelated RatesOptimization ProblemsCritical Points of Multivariable FunctionsCritical Points and Classification of ExtremaSecond Partial Test for Local Extrema (Hessian)The Hessian Matrix and Second Derivative TestUnconstrained Optimization: Finding ExtremaOptimization in Multiple VariablesLagrange MultipliersConstrained Optimization and Lagrange MultipliersUtility and PreferencesMarginal Utility and Diminishing ReturnsProfit MaximizationPerfect CompetitionShutdown and Breakeven DecisionsMonopolyMonopolistic CompetitionOligopoly and Strategic BehaviorGame Theory BasicsNash EquilibriumNash Equilibrium RefinementsStrategic Form Games and Nash EquilibriumMixed Strategies and Probabilistic PlayRepeated Games and Trigger StrategiesCartels and Collusion: Cooperation in OligopolyCollusion, Cartels, and Stability

Longest path: 105 steps · 529 total prerequisite topics

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