Nash Equilibrium Solver
Solves a two-player game in strategic form: enter each player’s payoff matrix and get every pure-strategy Nash equilibrium (by best-response check) and the mixed equilibria found by support enumeration, together with expected payoffs, each player’s maximin (security) value and the strategies removed by iterated elimination of strictly dominated strategies. Zero-sum games are detected and their minimax value is reported. Games up to 6×6.
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Results
Notes
- A Nash equilibrium is a strategy profile where no player can gain by deviating unilaterally. Nash’s theorem guarantees every finite game has at least one equilibrium, possibly in mixed strategies.
- Support enumeration tries every pair of equal-size strategy supports and solves the indifference equations on each; it finds all equilibria of non-degenerate games, but in degenerate games (with tied best responses) equilibria can form a continuum of which only representatives are shown.
- In a zero-sum game the equilibrium payoff is the minimax value of von Neumann’s theorem, and it coincides with both players’ security values.
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