2×2 Nash

A chooses the top or bottom row; B chooses the left or right column. Each cell contains their respective payoffs. Choose an example or edit any number, then calculate. Highlighted individual inputs are best responses; a marked cell is a mutual best response, hence a pure equilibrium.

The result lists all equilibrium points and intervals. P(Top) and P(Left) are the probabilities of the first strategies; 0% chooses the second strategy, 100% the first. Any pair of probabilities within the intervals in one row is an equilibrium. E[A] and E[B] are the expected payoffs or their ranges. Intervals include their endpoints. The solver checks all nine support combinations, including weak dominance and boundary ties.

Finite payoffs use floating-point arithmetic. Very different magnitudes or nearly equal values can lose precision; displayed numbers are rounded. The examples describe mathematical games, not predictions of real decisions.