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Analyze strategic interactions and find Nash equilibria
Select a preset or configure your own matrix
Each cell shows Player 1 / Player 2 payoffs
Named after John Nash, a Nash equilibrium is a strategy profile where no player can unilaterally improve their payoff. It is the cornerstone of modern game theory, underpinning auction design, pricing strategy, and international relations.
The archetypal example of how individual rationality produces collectively suboptimal outcomes. Both players have a dominant strategy to defect, yet mutual defection (1,1) is worse than mutual cooperation (3,3) — the defining tension of social dilemmas.
Game theory informs economics, political science, evolutionary biology, computer science, and military strategy. Key applications include mechanism design for auctions, voting system analysis, firm pricing decisions, and modelling arms races.
A strategy is strictly dominated if another strategy always yields a higher payoff regardless of what opponents do. Rational players never play dominated strategies, and iterative elimination (IESDS) often uniquely solves the game.