Game theory is the study of strategic decisions, where your best move depends on what someone else does. Its most famous example, the prisoner's dilemma, shows two players each choosing what is individually rational, and both ending up worse off than if they had cooperated. In economics it explains why firms in an oligopoly fall into price wars, why cartels like OPEC are unstable, and why advertising spending escalates. The key ideas are the dominant strategy, the move that is best whatever the rival does, and the Nash equilibrium, the outcome where no one can do better by changing alone.
Picture two petrol stations facing each other across a road. If both keep prices high, both do nicely. But each is tempted to undercut the other and steal the customers, so each cuts a little, then a little more, until they are matching each other to the cent and both are earning far less than they would have if they had just left prices alone. Nobody made them do it. They reasoned their way into a worse outcome, each one acting sensibly. That is the puzzle at the heart of game theory, and it is one of the most useful ideas in the whole subject.
Game theory is the study of strategic interdependence, situations where the best choice for you depends on what someone else chooses. It was built by economists and mathematicians, and in the A level syllabus it lives under oligopoly, the market structure where a few large firms watch each other constantly. Understand the basic game and you understand why those firms behave the way they do.
The prisoner's dilemma
The classic set up, the one the whole idea is named after, is two suspects questioned in separate rooms. Each is offered a deal to betray the other. If both stay silent they get a light sentence; if both betray they get a heavy one; if one betrays and the other stays silent, the betrayer walks free and the silent one takes the worst sentence of all. The trap is that betraying is the safer move whatever the other person does, so both betray, and both end up worse off than if they had trusted each other. Swap the prisoners for two firms and silence for keeping prices high, and you have the economics version.
| Firm B holds its price high | Firm B cuts its price | |
|---|---|---|
| Firm A holds its price high | Both do well: steady, healthy profits for each | A loses customers to B: A does badly, B does very well |
| Firm A cuts its price | A wins customers from B: A does very well, B does badly | Price war: both end on thin margins, worse than the top left |
A price war as a prisoner's dilemma. Each firm's safest individual move is to cut, so both cut and land in the bottom right, worse off than the cooperative top left.
Read the grid the way each firm does. If your rival holds their price high, you do best by cutting and taking their customers. If your rival cuts, you cannot afford to hold high and lose everyone, so again you cut. Cutting is the better move whatever the rival does. That is a dominant strategy, and because both firms have it, both cut, landing in the bottom right cell: the price war that leaves them both worse off than the top left cell they could have shared. Neither can improve by changing alone, which is what makes that cell stable.
- Interdependence
- In an oligopoly each firm's best decision depends on what its rivals do, so firms cannot plan in isolation. This is the whole reason game theory applies here.
- Dominant strategy
- A move that is your best response whatever the other player chooses. In the price war, cutting price is dominant, which is why both firms cut.
- Nash equilibrium
- An outcome where no player can do better by changing their choice alone. The price war cell is a Nash equilibrium, stable yet worse for both than cooperation.
Where you see it in the real economy
Once you can spot the shape, it is everywhere a few players watch each other. Petrol stations and supermarkets fall into price wars for exactly this reason, which is also why oligopoly prices are often sticky: nobody wants to cut and trigger the war, and nobody dares raise alone. Cartels like OPEC live the same dilemma from the other side. Members agree to restrict output and keep prices high, the cooperative top left cell, but each member is then tempted to quietly cheat and sell a little more at the high price, which is the individually dominant move. Because every member feels that pull, cartels are inherently unstable and tend to break down, which is the textbook evaluation point.
It reaches past firms, too. Two brands locked in an advertising arms race each spend more to avoid losing ground, and both end up spending heavily just to stand still, a prisoner's dilemma in marketing budgets. Even everyday life has the structure: two countries in an arms race, drivers deciding whether to merge politely, students deciding whether to stay late when everyone else does. The lesson is the same each time. Individually rational choices can add up to a collectively worse outcome, and seeing that is often the first step to designing a way out of it.
Individually rational choices can add up to a collectively worse outcome. That is the whole idea.
Game theory is your sharpest tool for an oligopoly question. Use it to explain price rigidity (firms fear starting a price war, so prices stay sticky), to explain the temptation to collude (the cooperative cell is better for the firms), and crucially to evaluate why collusion and cartels are unstable (each member has a dominant strategy to cheat). Draw or describe the payoff matrix, name the dominant strategy and the Nash equilibrium, and you have shown the examiner the interdependence that defines the market structure. A model sentence: "Because each firm has a dominant strategy to undercut, the Nash equilibrium is mutual price cutting, which explains both the instability of cartels and the price rigidity firms adopt to avoid triggering a war."
- Game theory is the study of strategic interdependence, where your best move depends on what a rival does. In the syllabus it sits under oligopoly.
- The prisoner's dilemma shows two players each choosing rationally and both ending up worse off than if they had cooperated.
- A dominant strategy is your best move whatever the rival does; when both players have one, you reach a Nash equilibrium.
- It explains real behaviour: oligopoly price wars and price rigidity, unstable cartels like OPEC, and advertising arms races.
- For the exam, use the payoff matrix to explain interdependence, price rigidity, and why cartels tend to break down.
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Frequently asked
What is game theory in economics?
Game theory is the study of strategic decision making, where the best choice for one player depends on what other players choose. In economics it is used mainly to analyse oligopoly, the market structure with a few large interdependent firms, because there each firm must anticipate how rivals will react to its pricing, output or advertising. Its central tools are the payoff matrix, the dominant strategy, the move that is best whatever the rival does, and the Nash equilibrium, an outcome where no player can improve by changing alone. The famous prisoner's dilemma is its best known example.
What is the prisoner's dilemma?
The prisoner's dilemma is the classic game in which two players each make the individually rational choice and both end up worse off than if they had cooperated. Two suspects, questioned separately, each do better by betraying the other whatever the other does, so both betray and both get a heavy sentence, when staying silent would have served them better. In economics the same structure explains a price war: two firms each find it safest to cut prices, so both cut and both earn less than if they had kept prices high.
How is game theory used in oligopoly?
It explains the behaviour that defines an oligopoly: interdependence. Game theory shows why oligopoly prices are often rigid, since no firm wants to cut and start a price war or raise alone and lose customers; why firms are tempted to collude, since the cooperative outcome is more profitable for them; and crucially why cartels are unstable, since each member has a dominant strategy to cheat on the agreement. Using a payoff matrix to show the dominant strategy and the Nash equilibrium is one of the strongest ways to analyse and evaluate an oligopoly question.
What is a Nash equilibrium?
A Nash equilibrium is an outcome of a strategic game in which no player can do better by changing their own choice while the others keep theirs unchanged. It is stable, but it is not necessarily the best outcome for the players collectively. In the price war version of the prisoner's dilemma, both firms cutting their prices is a Nash equilibrium, since neither can improve by unilaterally raising its price, even though both would be better off if they had jointly kept prices high. That gap between the stable outcome and the better cooperative one is exactly what makes the idea so useful.
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