Game Theory & Strategic Behaviour
CollegeChapter 10 mentioned that oligopolists behave "interdependently" and that cartels resemble a prisoner's dilemma. Game theory is the formal language for exactly this: how rational agents should act when the best choice depends on what everyone else chooses too.
At a glanceGames, strategies and Nash equilibrium
A game consists of players, the strategies available to each, and the payoffs each combination of strategies produces. A dominant strategy is one that is best for a player no matter what rivals do. A Nash equilibrium is a set of strategies, one per player, such that no player can improve their payoff by unilaterally switching strategy, given what everyone else is doing — it is a state of mutual best responses, not necessarily the best joint outcome.
| Firm B: Low price | Firm B: High price | |
|---|---|---|
| Firm A: Low price | A: 20, B: 20 | A: 50, B: 5 |
| Firm A: High price | A: 5, B: 50 | A: 35, B: 35 |
Here, Low price is dominant for both firms (it beats High price whatever the rival does), so (Low, Low) with payoffs (20, 20) is the Nash equilibrium — even though (High, High) with payoffs (35, 35) makes both firms better off. This gap between individually rational and jointly rational outcomes is the classic prisoner's dilemma, and it is exactly why the OPEC cartel of Chapter 10 is so hard to sustain.
Sequential games, credible threats, and repeated cooperation
When players move in sequence rather than simultaneously, the game is drawn as an extensive-form tree, and solved by backward induction: work out the best move at the last decision point first, then reason backward to the start. This often shows that a threat which looks intimidating is not credible, because carrying it out would hurt the threatener too.
A single prisoner's dilemma predicts non-cooperation. But if the same two players interact repeatedly — as real oligopolists and cartel members do — cooperation can become an equilibrium. A simple tit-for-tat or grim-trigger strategy (cooperate first, then punish any defection forever) sustains the jointly better outcome as long as players value the future enough. Formally, cooperation is sustainable when the discount factor δ satisfies:
This is the game-theoretic version of "the shadow of the future" — why real cartels sometimes hold together, and why trust between repeat trading partners substitutes for formal contracts.
Worked example: backward induction in a market-entry game
Q1Is a Nash equilibrium always the best possible outcome for the players?
No — the prisoner's dilemma is the standard counterexample. The Nash equilibrium (Low, Low) is not Pareto efficient: both players could be simultaneously better off at (High, High). Nash equilibrium describes what rational, self-interested players will actually do given no ability to make binding joint commitments — not what would be collectively best.
Q2Why do some cartels and duopolies avoid price wars in real life, if the dilemma logic predicts they should defect?
Because real interactions are usually repeated, not one-shot. If firms expect to face each other again and again, the threat of future punishment (a price war triggered by today's defection) can make honouring a high-price agreement individually rational — exactly the tit-for-tat / grim-trigger logic. This breaks down when firms discount the future heavily, or expect the interaction to end soon (e.g. a firm about to exit the market).
Q3What makes a threat "credible" in game theory?
A threat is credible only if carrying it out is actually in the threatener's own interest at the moment it must be carried out — i.e. it survives backward induction as part of a subgame-perfect equilibrium. An empty threat that would hurt the threatener more than compliance is rationally ignored by the other player, however loudly it is announced.
Q4How does game theory formalise the informal "kinked demand curve" idea from Chapter 10?
The kinked demand curve assumed rivals match price cuts but ignore price rises — an assumed reaction function. Game theory instead derives what rivals should rationally do as a best response, and asks whether that assumed behaviour is itself an equilibrium. It replaces an assumed rule of thumb with a testable equilibrium concept, which is why modern oligopoly theory is built on game theory rather than the older kinked-curve story.
How the ideas connect
Every key idea in this chapter, branching from the core concept — use it to see the whole picture at a glance.
The key facts, visualised
Worked problems, step by step
Follow each solution line by line, then try to reproduce it on paper before moving on.
Example 1Two firms choose High or Low price. Low price is a dominant strategy for both. What is the outcome?
- A dominant strategy is best regardless of the rival.
- If Low dominates for each firm, both play Low.
- The Nash equilibrium is both charging Low.
Example 2In a one-shot prisoners dilemma, why do both players defect even though mutual cooperation pays more?
- Whatever the rival does, defecting gives a higher individual payoff.
- So defect is the dominant strategy for each.
- Both defect, reaching a worse outcome than cooperating.
Now you try
Work each one out first, then tap to reveal the worked answer.