mathematics

Game Theory

The mathematics of strategic interaction — how rational agents make decisions when outcomes depend on what others do.

game theoryNash equilibriumprisoner's dilemmastrategyeconomicscooperation

Game theory is the mathematical study of strategic interaction between rational decision-makers. Pioneered by John von Neumann and Oskar Morgenstern in 1944, and revolutionized by John Nash's equilibrium concept in 1950, it has become essential to economics, political science, biology, and computer science.

At its core, game theory asks: what happens when your best choice depends on what others choose? The answer is often surprising — individually rational behavior frequently leads to collectively irrational outcomes. The Prisoner's Dilemma shows why cooperation is hard. The Tragedy of the Commons shows why shared resources get depleted. Auction theory shows why you should bid your true value.

These simulations let you experiment with the foundational models of game theory, see Nash equilibria emerge from strategic interaction, and discover why the 'rational' outcome is often not the 'good' outcome.

5 interactive simulations

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Auction Theory Simulator

Compare first-price, second-price (Vickrey), and English auctions — visualize bidding strategies, revenue, and efficiency with configurable bidder populations

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Evolutionary Stable Strategy (ESS) Simulator

Simulate the Hawk-Dove game with replicator dynamics — watch population frequencies converge to the evolutionarily stable strategy predicted by V/C

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Nash Equilibrium Visualizer

Explore mixed-strategy Nash equilibria in 2x2 bimatrix games with interactive best-response diagrams

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Iterated Prisoner's Dilemma Simulator

Simulate Axelrod-style tournaments with Tit-for-Tat, Always Defect, and Always Cooperate strategies competing across hundreds of rounds with configurable noise

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Tragedy of the Commons Simulator

Model resource depletion dynamics with competing herders — watch how cooperation percentage determines whether a shared resource collapses or sustains