Oligopoly: game theory, collusion and cartels

Two-firm game theory

A payoff matrix shows the outcome (usually profit) for two firms for each combination of strategies.

• A dominant strategy is the best choice whatever the rival does.
• A Nash equilibrium is a position where neither firm can gain by changing its strategy, given the other's choice.

The classic result (a 'prisoners' dilemma') is that each firm's dominant strategy leads to an outcome worse for both than if they had co-operated.

Profits in $m. Low price is the dominant strategy for each firm; the Nash equilibrium (5, 5) is worse for both than (10, 10).

Collusion and cartels

Collusion: firms co-operate instead of competing, to raise joint profits.

• Overt (formal) collusion: an explicit agreement on prices, output or market sharing. A formal group is a cartel (OPEC among countries is the best-known). Illegal in most countries for firms.
• Tacit collusion: no agreement, but firms avoid competing, for example by following a price leader (often the dominant or lowest-cost firm) whose price changes are copied.

Collusion is more likely with few firms, similar costs and products, high barriers, stable demand, and weak competition law.

Why collusion breaks down

Each member has an incentive to cheat: secretly cut price or raise output to gain share (moving from (10, 10) to (14, 2) in the matrix). Collusion also breaks down if demand falls, new firms enter, costs differ, or authorities detect it and impose fines. A breakdown can lead to a price war.

Costs and benefits of collusion to stakeholders

• Firms: higher, more stable profits; less risk. Risk of large fines.
• Consumers: higher prices, less choice and output, a transfer of consumer surplus to producers; but profits may fund some innovation.
• Workers: possibly job security, but lower output means fewer jobs.
• Government/society: allocative inefficiency and deadweight loss; some argue collusion on standards or research can be beneficial.

Worked example

Use the payoff matrix to find each firm's dominant strategy and the Nash equilibrium.

1. If B charges high, A gets 10 (high) or 14 (low): low is better.
2. If B charges low, A gets 2 (high) or 5 (low): low is better.
3. So low is A's dominant strategy; by symmetry, B's too.
4. Nash equilibrium: both low, earning $5m each, although both charging high would give $10m each.

Answer: Dominant strategy: low price; Nash equilibrium (low, low) = ($5m, $5m).

Check yourself

1. Using the matrix, how much more profit does each firm earn if both charge a high price than at the Nash equilibrium? Give your answer in $m.
   Show answer

   $5 m. 10 - 5 = $5m each.

2. Both firms agree to charge a high price. Firm A cheats and cuts its price while B keeps to the deal. By how much does A's profit rise, in $m?
   Show answer

   $4 m. A's profit rises from 10 to 14: a gain of $4m. This is the incentive to cheat.

3. What is the total joint profit of the two firms at the Nash equilibrium, in $m?
   Show answer

   $10 m. 5 + 5 = $10m, against $20m if they colluded.

4. A dominant strategy is
   • the strategy that gives the highest joint profit
   • the strategy chosen by the largest firm
   • the best strategy for a firm whatever its rival does
   • a strategy agreed in a cartel
   Show answer

   the best strategy for a firm whatever its rival does. It does not depend on the rival's choice.

5. Firms in an oligopoly follow the price changes of the market leader without any agreement. This is
   • tacit collusion through price leadership
   • an overt cartel
   • a price war
   • perfect competition
   Show answer

   tacit collusion through price leadership. No formal agreement, but co-ordinated behaviour.

6. Which factor makes a cartel most likely to break down?
   • There are very few members
   • Members have identical costs
   • Each member has an incentive to secretly increase output
   • Demand is stable
   Show answer

   Each member has an incentive to secretly increase output. Cheating gains share and profit for the cheat.

7. What is the main cost of collusion to consumers?
   • Higher prices and lower output
   • More choice
   • Lower prices
   • Faster innovation
   Show answer

   Higher prices and lower output. Colluding firms act like a joint monopoly.

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Sources

• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Economics specification (XEC11/YEC11), Unit 3 Business behaviour and Appendices 6 and 7
• Pearson Edexcel IAL Economics WEC13/01 mark scheme, January 2021

Last updated 8 November 2026. Spotted a mistake? Tell us.