Use this game-theory utility to inspect best responses or pure-strategy equilibria in a finite payoff model whose players, actions, and utilities are specified explicitly.

Row-player payoff matrix

Required list input.

Column-player payoff matrix

Required list input.

Find every pure-strategy Nash equilibrium in a finite two-player normal-form game, including tied best responses. Strategy indices are zero-based; mixed-strategy equilibria are not computed. The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.^[1]

Pure Nash equilibria

The resulting pure nash equilibria returned as an object.

• Pure equilibria may not exist or may be multiple, and best-response dynamics need not converge. Results depend on complete and accurate payoffs and do not by themselves predict behavior, learning, bargaining, or mixed strategies.
• Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.

Inspect mixed equilibria and sensitivity to payoff changes, and compare model predictions with institutional constraints or observed behavior.

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