Game Theory

Definition

Game theory is the mathematical study of strategic interaction — situations in which each participant’s best choice depends on what others choose. A “game” in this technical sense has: players (decision-makers), strategies (the complete set of actions each player can take), and payoffs (what each player earns for each combination of strategies).

Game theory was formalized in the 1940s by John von Neumann and Oskar Morgenstern, and extended by John Nash, whose concept of equilibrium became the field’s central analytical tool. It was developed largely to explain economic behavior under oligopoly, but its reach extends to evolutionary biology, political science, international relations, auction design, and everyday negotiation.

Why it matters

Key takeaways

The Prisoner's Dilemma is the central parable: each player has a dominant strategy (defect) that leads to a collectively worse outcome than mutual cooperation — an equilibrium that is individually rational but collectively suboptimal.
Nash equilibrium: a set of strategies where no player can improve their payoff by unilaterally changing their own strategy, given what others are doing. Every finite game has at least one Nash equilibrium.
Dominant strategy: an action that is best for a player regardless of what opponents do. When all players have dominant strategies, predicting behavior is straightforward.
Repeated games change the calculus: the threat of future retaliation can sustain cooperation that would collapse in a one-shot interaction.
Commitment devices resolve strategic problems by credibly constraining future options — eliminating the temptation to defect and making cooperation credible to rivals.
Applications span: oligopoly pricing, arms races, international trade negotiations, auctions, evolutionary dynamics, voting systems, and corporate strategy.

The Prisoner’s Dilemma

Read it as: The green path (both cooperate) produces the best joint outcome, but neither player can unilaterally achieve it — if you cooperate and your opponent defects, you get the worst outcome (0). The dominant strategy is to defect regardless of what the other player does. Both playing the dominant strategy produces the red Nash equilibrium: worse for everyone than cooperation, but individually rational given the other’s strategy.

Nash equilibrium and dominant strategies

Nash equilibrium defined

A Nash equilibrium is a stable outcome — no player can improve their payoff by unilaterally changing their strategy, given what everyone else is doing. It does not require that players communicate or coordinate; it is simply a state where everyone is doing their best given the actual strategies of others.

Not all Nash equilibria are equal. Some are Pareto-efficient (no player can be made better off without making another worse off); some are not, as the Prisoner’s Dilemma illustrates. Game theory predicts which equilibrium will emerge in a given game structure, but it does not guarantee that equilibria are socially desirable.

When dominant strategies exist

In the Prisoner’s Dilemma, defecting is a dominant strategy — better regardless of what the other player does. When all players have dominant strategies, predicting the outcome is straightforward: each player plays their dominant strategy, and the result is a Nash equilibrium in dominant strategies. The problem is that this equilibrium may be worse for everyone than alternatives that would require coordination.

Repeated games and cooperation

The one-shot Prisoner’s Dilemma leads to universal defection. But in repeated games — where players interact multiple times with ongoing reputation — cooperation can emerge and be sustained through reciprocity strategies.

The most robust of these is tit-for-tat: cooperate on the first move, then mirror whatever your opponent did last round. This strategy is never the first to defect, punishes defection immediately, and forgives after punishment. In computer tournaments simulating repeated Prisoner’s Dilemmas, tit-for-tat consistently outperforms more exploitative strategies over long interactions.