Introduction

Game theory is the study of strategic interactions — situations where the outcome for each participant depends not only on their own decisions, but also on the decisions of others. It is one of the most powerful analytical tools in economics, used to model competition between firms, negotiations between countries, auctions, and much more.

What is a “Game” in Economics?

In game theory, a “game” is any situation involving:

• Players — the decision makers (firms, individuals, governments)
• Strategies — the available choices or actions each player can take
• Payoffs — the outcomes (profits, utility, years in prison) each player receives depending on the combination of strategies chosen
• Rules — the structure of the interaction (who moves when, what information is available)

In economics, players are assumed to be rational — they aim to maximise their own payoff. Actions might include: how much to produce, what price to charge, whether to cooperate or compete, or whether to invest in advertising.

Two Ways to Represent a Game

1. Normal Form (Strategic Form)

The normal form presents a game as a matrix (table) showing all possible combinations of strategies and their resulting payoffs. All players choose their strategies simultaneously. This is most useful for one-shot or simultaneous games.

2. Extensive Form

The extensive form represents a game as a decision tree, showing the sequence of moves, who moves when, and what each player knows at each decision point. This is most useful for sequential games where players move one after another.

The Prisoner’s Dilemma — The Most Famous Game

The Prisoner’s Dilemma perfectly illustrates why rational individuals may fail to cooperate, even when cooperation would leave both better off.

The Setup

Two suspects, John and Edward, are arrested and held in separate cells. Each is offered the same deal: confess or deny. They cannot communicate. The payoffs (in years in prison — lower is better) are:

Analysis — The Nash Equilibrium

Consider John’s thinking:

• If Edward confesses → John is better off confessing (4 years) than denying (6 years)
• If Edward denies → John is better off confessing (0 years) than denying (1 year)

So confessing dominates denying for John — regardless of what Edward does. By the same logic, Edward also chooses to confess. The result: both confess and each gets 4 years.

Yet if both had denied, each would only get 1 year — a much better outcome for both. This is the central paradox of the Prisoner’s Dilemma: individually rational decisions lead to a collectively worse outcome.

Nash Equilibrium

Named after mathematician John Nash, a Nash Equilibrium is a situation where no player can improve their payoff by unilaterally changing their strategy, given the strategy of the other player(s). In the Prisoner’s Dilemma, (Confess, Confess) is the Nash Equilibrium — neither player benefits from switching alone.

Nash Equilibrium: A set of strategies where no player has an incentive to deviate unilaterally.

Dominant Strategy

A dominant strategy is one that gives a player the highest payoff regardless of what the other player does. In the Prisoner’s Dilemma, “Confess” is a dominant strategy for both players. When all players have a dominant strategy, the outcome is called a dominant strategy equilibrium.

Applications in Economics

Game theory is widely used to analyse real-world economic situations:

• Oligopoly competition: Firms deciding whether to cut prices or maintain them (e.g., the OPEC cartel problem)
• Advertising: Two firms deciding whether to advertise — a classic Prisoner’s Dilemma structure
• Trade policy: Countries deciding whether to impose tariffs
• Auctions: Bidders strategically deciding how much to bid
• Wage bargaining: Workers and employers negotiating contracts

Cooperative vs. Non-Cooperative Games

• Non-cooperative games: Players act independently, pursuing their own self-interest. Most game theory (including the Prisoner’s Dilemma) is non-cooperative.
• Cooperative games: Players can form binding agreements and coalitions. The focus is on which coalitions form and how payoffs are divided.

Repeated Games and Cooperation

In a one-shot game, rational players defect (as in the Prisoner’s Dilemma). But in repeated games — where the same players interact over and over — cooperation can emerge. Players can use strategies like tit-for-tat (cooperate first; then do whatever the opponent did last round) to sustain cooperation, because the threat of future punishment deters defection.

This explains why cartels often hold together in industries where firms interact repeatedly, despite the incentive to cheat.

Summary

Game theory provides a rigorous framework for analysing strategic decision-making. Its core concepts — players, strategies, payoffs, Nash equilibrium, and dominant strategies — are essential tools for any economist studying competition, bargaining, or policy. The Prisoner’s Dilemma remains its most celebrated example, demonstrating that individual rationality does not always produce socially optimal outcomes.