Game theory for oligopoly (HL only)
IB Economics HL· 15 min read
1. Core Concepts of Game Theory★★☆☆☆⏱ 15 min
In oligopoly, there are only a few large firms, so each firm’s pricing, output, and advertising decisions directly impact the profits of competing firms. This interdependence means firms must anticipate rivals’ actions when making their own choices, which is exactly what game theory is designed to model.
Game Theory
A framework for analyzing strategic decision-making between interdependent players (firms, in the context of oligopoly)
Example:
Two airlines deciding whether to raise or lower ticket prices
All games have three core components:
Players: The decision-makers (firms in oligopoly interactions)
Strategies: All possible choices available to each player (e.g. high price / low price)
Payoffs: The outcome (usually profit) for each combination of chosen strategies
Two coffee shop chains, A and B, are deciding whether to price their signature latte at $4 or $5. Identify the core components of this game.
- 1
Players are the two decision-makers in the interaction: Chain A and Chain B.
- 2
Strategies for each player are the two possible pricing choices: Price at $4, or price at $5.
- 3
Payoffs are the weekly profit each chain earns for each combination of choices, displayed in a payoff matrix where the first number in each cell is the row player's payoff, and the second is the column player's.
Exam tip:
In all IB Economics exams, payoffs always list the row player's outcome first. Double-check which player is which before solving any problem.
2. Dominant Strategy and the Prisoner's Dilemma★★★☆☆HL only⏱ 20 min
A dominant strategy is a choice that gives a player a higher payoff no matter what the other player chooses. The prisoner's dilemma is the most common game tested in IB Economics, used to show why collusive agreements between oligopolies are often unstable.
Prisoner's Dilemma
A non-cooperative game where both players have a dominant strategy that leads to a Pareto-inferior outcome (both players would be better off if they cooperated)
Example:
Two oligopolists deciding whether to stick to a collusive high price or cheat on the agreement
Two oil companies, X and Y, have agreed to collude to keep prices high. Each can either Stick to the agreement (high price) or Cheat (low price). Payoffs are annual profit in millions of $. Find the dominant strategy for each firm.
- 1
First, map the payoff matrix for the game:
- 2
- 3
Find X's best response to each of Y's choices: If Y sticks: X earns 10 for sticking, 12 for cheating, so X prefers to cheat. If Y cheats: X earns 3 for sticking, 5 for cheating, so X still prefers to cheat.
- 4
Repeat for Y: If X sticks: Y earns 10 for sticking, 12 for cheating. If X cheats: Y earns 3 for sticking, 5 for cheating. Y also prefers to cheat in both cases.
- 5
Conclusion: Cheating is a dominant strategy for both X and Y, because it gives the highest payoff regardless of the opponent's choice.
3. Nash Equilibrium★★★★☆HL only⏱ 20 min
A Nash equilibrium is a stable outcome of a game where no player can improve their own payoff by changing their strategy, if the other player's strategy stays the same. Every dominant strategy equilibrium is a Nash equilibrium, but not all Nash equilibria are dominant strategy equilibria.
Nash Equilibrium
A stable game outcome where neither player can increase their payoff by changing their own strategy unilaterally
Example:
The outcome (Cheat, Cheat) in the prisoner's dilemma oil company game above is a Nash equilibrium
Find the Nash equilibrium for the oil company collusive game from the previous example.
- 1
Check the (Stick, Stick) outcome: Can X improve their payoff by switching to Cheat if Y stays on Stick? Yes: 12 > 10, so this is not a Nash equilibrium.
- 2
Check the (Stick, Cheat) outcome: Can X improve switching to Cheat if Y cheats? Yes: 5 > 3, so this is not an equilibrium.
- 3
Check the (Cheat, Stick) outcome: Can Y improve switching to Cheat if X cheats? Yes: 5 > 3, so this is not an equilibrium.
- 4
Check the (Cheat, Cheat) outcome: Can X improve switching to Stick if Y cheats? No: 3 < 5. Can Y improve switching to Stick if X cheats? No: 3 < 5. Neither can improve their payoff unilaterally, so (Cheat, Cheat) is the Nash equilibrium.
Exam tip:
To find Nash equilibrium, test every cell in the payoff matrix: if neither player would want to change their choice when the other's choice is fixed, it is a Nash equilibrium.
4. Applications of Game Theory to Oligopoly★★★☆☆HL only⏱ 15 min
Game theory can be applied to many strategic decisions that oligopolistic firms make beyond just pricing and collusion. Common applications covered in IB exams include advertising decisions, entry into new markets, and investment in production capacity.
Two soft drink firms are deciding whether to launch a large national advertising campaign. If both advertise, each earns $100m profit; if neither advertises, each earns $150m profit; if one advertises and the other doesn't, the advertising firm earns $200m and the non-advertising firm earns $50m. Find the Nash equilibrium.
- 1
Set up the payoff matrix with Coca-Cola as the row player:
- 2
- 3
Confirm dominant strategies: For Coca-Cola, advertising gives a higher payoff whether Pepsi advertises or not. The same is true for Pepsi, so advertising is a dominant strategy for both.
- 4
Check equilibrium: At (Advertise, Advertise), neither firm can improve their profit by switching to no advertising, so this is the Nash equilibrium.
- 5
Conclusion: This is another prisoner's dilemma: both firms would be better off if neither advertised, but individual incentives lead both to advertise, resulting in lower overall profit.
5. Common Pitfalls
Wrong move:
Mixing up the order of payoffs, using the column player's payoff for the row player
Why:
IB problems always list the row player's payoff first; reversing order leads to wrong strategy conclusions
Correct move:
Always confirm which player is the row player, and that the first number in each cell belongs to the row player before starting analysis
Wrong move:
Claiming all Nash equilibria are bad outcomes for both players
Why:
This is only true for prisoner's dilemma games, not all games
Correct move:
Analyze the payoffs given in the question to find the equilibrium, do not rely on memorized outcomes
Wrong move:
Stating that collusion is always impossible in oligopoly because of the incentive to cheat
Why:
This result only applies to one-shot games; repeated games allow for punishment strategies that sustain collusion
Correct move:
Acknowledge that collusion is unstable in one-shot interactions, but can be sustained in repeated interactions between firms
Wrong move:
Claiming no dominant strategy means no Nash equilibrium exists
Why:
Many games have no dominant strategies but still have one or more Nash equilibria
Correct move:
Always test every cell for Nash equilibrium even if you do not find a dominant strategy for either player
6. Quick Reference Cheatsheet
Concept | Definition | IB Exam Tip |
|---|---|---|
Dominant Strategy | Highest payoff regardless of opponent's choice | Check best response for both opponent choices to confirm |
Prisoner's Dilemma | Dominant strategy leads to worse collective outcome | Most common question: explains cartel instability |
Nash Equilibrium | No player can improve payoff unilaterally | Test all cells: if no player wants to switch, it's equilibrium |
Payoff Matrix Order | First = row player, second = column player | Reversing this is the most common exam mistake |
When this came up on past exams
AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.
- 2024 · Paper 1
10 mark on prisoner's dilemma
- 2022 · Paper 2
Data response on game theory
- 2019 · Paper 1
15 mark on Nash equilibrium
What's Next
Game theory is a core HL microeconomic concept that underpins all analysis of strategic behavior in oligopoly, a frequently tested topic on both Paper 1 and Paper 2 of the IB Economics exam. It explains why cartels are unstable, why firms overinvest in advertising, and how strategic interdependence shapes firm behavior in concentrated markets. This knowledge lays the foundation for understanding repeated games, entry deterrence, and government regulation of oligopolies. You can now build on this foundation by exploring related topics in oligopoly and market regulation.