CFA Level I Exam · The Firm and Market Structures

Oligopoly and Game Theory for CFA Level I

Updated 5 October 2026 · Fact-checked

An oligopoly is a market with a few large firms whose decisions depend on each other. Game theory models that interdependence. To solve questions, identify each firm's best response, find the Nash equilibrium where neither firm gains by changing strategy alone, and compare it with the collusive outcome, which is usually unstable because each firm can cheat.

Understand Oligopoly and Game Theory

An oligopoly is a market with a small number of firms, high barriers to entry, and products that are either identical or differentiated. The key feature is interdependence. Your profit depends on what your rivals do, and their profit depends on what you do. A perfectly competitive firm or a monopolist does not face this problem.

Because of interdependence, no single demand curve describes the market for one firm. Economists use models that make different assumptions about how rivals react. The kinked demand curve assumes rivals match a price cut but ignore a price rise. Demand is then elastic above the kink and less elastic below it, so marginal revenue has a gap. Marginal cost can move within that gap without changing price or output. This explains why prices in some oligopolies look sticky. The model does not explain how the starting price is set.

Three models are about how firms compete. In the Cournot model, firms choose quantities at the same time, each taking the rival's quantity as given. In the Bertrand model, firms with identical products choose prices at the same time, and price is driven down to marginal cost. In the Stackelberg model, one firm (the leader) commits to quantity first and the follower reacts. The leader gains from moving first. Cournot and Stackelberg outcomes lie between the monopoly and perfectly competitive outcomes.

Game theory gives the general tool. A game has players, strategies and payoffs. A dominant strategy is best whatever the rival does. A Nash equilibrium is a set of strategies where no player can improve their payoff by changing only their own strategy. In the prisoner's dilemma, each player has a dominant strategy to defect (for example, cut price), so the Nash equilibrium leaves both worse off than if both had cooperated.

Firms can try to collude, by agreeing on output or price as a cartel, to earn monopoly-like profit. Each member then has an incentive to cheat, because secretly producing more raises its own profit. Collusion is easier to sustain with few firms, similar costs, identical products, repeated dealings and good detection and punishment of cheaters. In many jurisdictions explicit collusion is illegal.

Key formulas to remember

Nash equilibrium (rule): Each player's strategy is a best response to the other players' strategies; Test it by asking whether any one player gains by deviating alone. If none does, it is a Nash equilibrium. A game can have more than one.
Dominant strategy (rule): Payoff from strategy X ≥ payoff from any other strategy, whatever the rival does; If a player has a dominant strategy, they will play it. Not every game has one.
Cournot with linear demand and constant marginal cost: P = a − bQ; MC = c; n identical firms: each q = (a − c) ÷ [b(n + 1)]; total Q = n(a − c) ÷ [b(n + 1)]; For n = 1 this gives the monopoly output (a − c) ÷ 2b. As n grows, Q approaches the competitive output (a − c) ÷ b. Mainly useful for understanding. Most exam items are conceptual.
Bertrand equilibrium (identical products): P = MC; Holds for identical products, no capacity limits and similar costs. Price competition removes economic profit.
Kinked demand marginal revenue: MR has a vertical gap at the kink; if MC stays within the gap, price and quantity do not change; Above the kink demand is elastic (rivals do not follow a price rise). Below it demand is less elastic (rivals follow a cut).
Stackelberg ordering: Leader output > Cournot output > follower output; The leader moves first and earns more than the follower. Total output is greater than in Cournot, so price is lower.

How to solve Oligopoly and Game Theory questions

Use this method for any oligopoly or game theory question. It works for word questions and for payoff matrices.

1Read the stem and find what firms choose (price or quantity), and whether they choose at the same time or in sequence.
2Match the setting to a model. Simultaneous quantities means Cournot. Simultaneous prices with identical products means Bertrand. A leader that moves first means Stackelberg. Rivals that match cuts but not rises means kinked demand.
3For a payoff matrix, find each player's best response to each rival choice. Mark the higher payoff for the row player in each column, then for the column player in each row.
4The Nash equilibrium is the cell where both payoffs are marked. Check for any dominant strategy.
5Compare with the cooperative outcome. If both would be better off cooperating but each is tempted to deviate, it is a prisoner's dilemma.
6Judge stability of any collusion. Look at the number of firms, cost differences, product similarity, repeated play and ability to detect cheating.
7Eliminate two options by checking against the model's known ranking, for example monopoly price > Cournot price > competitive price, and pick the remaining one.

Quickest way: Best-response tick method for payoff matrices

When to use it: Use it for any two-player, two-strategy payoff matrix question. It takes under a minute.

For each column, tick the row player's higher payoff.
For each row, tick the column player's higher payoff.
A cell with two ticks is a Nash equilibrium.
If the double-tick cell pays less to both than another cell, you have a prisoner's dilemma.
For conceptual questions, memorise: Cournot = quantity, Bertrand = price and P = MC, Stackelberg = leader first, kinked = sticky price.

Common mistakes in Oligopoly and Game Theory

Calling the best joint outcome the Nash equilibrium.
Students look for the cell with the highest total payoff rather than testing for unilateral deviation.
Fix: Apply the deviation test. The Nash equilibrium is where no player gains by changing alone, and it may be worse for both than another cell.
Mixing up Cournot and Bertrand.
Both are simultaneous-move models with the same rivals, so they sound alike.
Fix: Cournot firms choose quantity. Bertrand firms choose price, and with identical products the price falls to marginal cost.
Thinking the kinked demand curve predicts the price level.
The diagram looks like a full pricing model.
Fix: It explains price stability, not how the price was set. Rivals follow cuts but not rises, which creates a gap in marginal revenue.
Assuming collusion is stable because it is profitable.
Students focus on the joint profit and forget each member's incentive to cheat.
Fix: Each member earns more by cheating if the others stick to the agreement. Stability needs few firms, detection and punishment, and repeated interaction.
Saying the Stackelberg follower earns more than the leader.
Students think the follower has more information.
Fix: The leader's commitment lets it take a larger share. Leader output is higher and follower output is lower than in Cournot.
Ordering the outcomes wrongly when comparing models.
Students forget that more competition means lower price and higher quantity.
Fix: Price falls and quantity rises as you move from monopoly or a cartel to Cournot, then Bertrand or perfect competition.

Worked examples

Example 1

Two firms, A and B, each choose a High price or a Low price. Payoffs (A, B) in $ millions: High/High = (10, 10); A High, B Low = (4, 14); A Low, B High = (14, 4); Low/Low = (6, 6). The firms act at the same time. What is the combined profit at the Nash equilibrium? A) $12 million B) $18 million C) $20 million

Show the solution

Find A's best responses. If B plays High, A gets 10 from High and 14 from Low, so Low. If B plays Low, A gets 4 from High and 6 from Low, so Low.
Find B's best responses. The matrix is symmetric, so B's best response is Low in both cases.
Low is a dominant strategy for both firms, so the Nash equilibrium is Low/Low with payoffs (6, 6).
Combined profit = 6 + 6 = $12 million.
Check the contrast: High/High gives 20 in total and would be better for both, but each firm gains by cutting its price alone. This is a prisoner's dilemma.

Answer: A) $12 million

Example 2

Market demand is P = 100 − Q and each firm has constant marginal cost of 20. Two identical firms choose quantities at the same time (Cournot). What is the equilibrium market price? A) $20.00 B) $46.67 C) $60.00

Show the solution

Firm 1's profit is (100 − q1 − q2 − 20) × q1 = (80 − q1 − q2) × q1.
Maximise by setting marginal profit to zero: 80 − 2q1 − q2 = 0, so q1 = (80 − q2) ÷ 2.
By symmetry q1 = q2 = q, so 80 − 3q = 0 and q = 26.67.
Total output Q = 2 × 26.67 = 53.33.
Price = 100 − 53.33 = $46.67.
Sense check: monopoly would give Q = 40 and P = 60. Perfect competition would give P = MC = 20. The Cournot price lies between them.

Answer: B) $46.67

Exam tips

Questions are mostly conceptual. Know the assumption behind each model: Cournot (quantity), Bertrand (price), Stackelberg (sequential), kinked demand (asymmetric reactions).
Use the ranking monopoly or cartel price > Cournot price > Bertrand or competitive price to eliminate options quickly.
For payoff matrices, apply the tick method. Do not spend time on arithmetic beyond adding the payoffs in the equilibrium cell.
Watch the exact wording on the Nash equilibrium: a state where no player can improve by changing only its own strategy. Expect distractors that describe a joint optimum.
In collusion questions, look for the stability factors in the stem, such as few firms, similar costs and repeated play, and pick the answer that matches.

Practice questions from The Firm and Market Structures

Oligopoly and Game Theory in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Oligopoly and Game Theory: frequently asked questions

What is the difference between Cournot, Bertrand and Stackelberg models?

Cournot firms choose quantities at the same time. Bertrand firms choose prices at the same time, and with identical products price falls to marginal cost. In Stackelberg, a leader chooses quantity first and the follower responds, so the leader earns more.

What is a Nash equilibrium in simple terms?

It is an outcome where each player is doing the best it can, given what the others are doing. No player can gain by changing its own strategy alone. It need not be the best outcome for the players as a group.

Why does the prisoner's dilemma matter for oligopoly?

It shows why collusion tends to break down. Both firms would earn more by keeping prices high, but each can earn more by cutting its price while the other holds. The result is a lower-profit Nash equilibrium unless cheating can be detected and punished.

Why is there a gap in marginal revenue on the kinked demand curve?

The curve has two segments with different slopes, one above the kink and one below. Each segment has its own marginal revenue curve, so MR jumps at the kink's quantity. Marginal cost can move within that gap without changing the profit-maximising price and output.