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2×2 Nash Equilibrium

Find mixed-strategy Nash equilibrium for a 2×2 bimatrix game.

Payoff Matrix (Player 1, then Player 2)

Row player payoffs A, Column player payoffs B

Result

Enter payoffs.

Technical Description & Theory

What is Game Theory Nash Equilibrium Calculator and Why it Matters?

A Nash equilibrium is a strategy profile in which no player benefits by unilateral deviation. Mixed equilibria of 2×2 games are found by indifference.

Mathematical Formula and Theory

Equalize expected payoffs of pure strategies in the support to obtain the mixing probabilities p and q.

How to Use This Calculator - Step by Step

  • Enter the four payoffs for each player.
  • Click Find Nash.

Solved Example with Full Calculation

Row [[2,0],[1,3]], Column [[1,0],[0,2]] yields mixed equilibrium p≈0.67, q≈0.33.