Nash Equilibrium Finder

2-player matrix games — pure and mixed strategy equilibria

Payoff Matrix — (Row payoff, Col payoff)

Row player: blue | Col player: orange

Mixed Strategy Simplex

p = P(Row plays strategy 1), q = P(Col plays strategy 1)

Click "Find Nash Equilibria" to analyze the game.

A Nash equilibrium (s*, t*): u₁(s*,t*) ≥ u₁(s,t*) for all s, and u₂(s*,t*) ≥ u₂(s*,t) for all t

A Nash equilibrium is a strategy profile where no player can improve their payoff by unilaterally deviating. Pure strategy NE: each player plays a single strategy. Mixed strategy NE: players randomize. By Nash's theorem (1950), every finite game has at least one NE (in mixed strategies). The support enumeration method finds all NE by checking which strategy subsets can be in a mixed NE.