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fin.game-theory-nash-equilibrium Calculator
Finds Nash equilibria in a 2×2 game matrix from each player's payoffs, and identifies dominant strategies. The Prisoner's Dilemma is the most famous Nash equilibrium — both players defect despite mutual cooperation being the socially optimal outcome.
Inputs
Payoff A Cooperate
Amount per unit of time or per unit quantity. Check the denominator before interpreting.
Payoff A Defect If B Coop
Amount per unit of time or per unit quantity. Check the denominator before interpreting.
Payoff A Coop If B Defect
Amount per unit of time or per unit quantity. Check the denominator before interpreting.
Payoff A Both Defect
Reference formula or conversion factor shown for context.
Results
dominant strategy for A
The value at the specified point or condition.
is this a Prisoner Dilemma?
Sample size or count used in the calculation.
Nash equilibrium
Sample size or count used in the calculation.
socially optimal
Reference formula or conversion factor shown for context.
Nash inefficiency
Useful output divided by total input, as a percentage. True 100% efficiency is impossible — losses appear as heat. LEDs: 30–50%. Electric motors: 85–97%. Switching supplies: 85–95%.