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Dominant Strategy Finder

Enter the row player's payoffs to check for a dominant strategy.

How it is calculated

You enter the row player's payoff for each of the four cells of a 2×2 game: strategy A against the opponent's left (al) and right (ar) moves, and strategy B against left (bl) and right (br). The tool subtracts row B from row A in each column, al − bl and ar − br. A dominates B if both differences are zero or positive and at least one is strictly positive; B dominates A in the mirror case. The result is Strategy A when A dominates, Strategy B when B dominates and None when neither does, including the case where the rows are identical. Dominance here is weak, not strict: a tie in one column still counts if the other column is strictly better. Only the row player's payoffs are used. Payoffs are unitless, so use the same unit throughout.

Worked example

Two suspects are interrogated separately. Payoffs are years in prison as negative numbers, so a higher number is better. Strategy A is confess, B is stay silent. If the other suspect confesses, A gives −5 and B gives −10. If the other stays silent, A gives 0 and B gives −1. The differences are −5 − (−10) = 5.00 in the left column and 0 − (−1) = 1.00 in the right column. Both are positive, so the result is Strategy A: confessing dominates, whatever the other suspect does.

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Common mistakes

  • Entering penalties such as prison years or costs as positive numbers. The tool treats larger as better, so enter them as negatives (−5, not 5) or the dominance will point to the worst strategy.
  • Mixing up rows and columns. The first letter is your strategy (A or B) and the second is the opponent's move (left or right), so ar is A against the opponent's right move.
  • Entering the opponent's payoffs. Only the row player's own payoffs are compared; the column player's side of a Nash analysis has to be checked separately by swapping roles.
  • Reading None as meaning no good strategy exists. It only means neither row beats the other in every column, as with A = (3, 1) and B = (2, 4); then the best choice depends on what you expect the opponent to do.
  • Expecting a strict result. If A = (3, 1) and B = (3, 0), the tool still returns Strategy A because A is never worse and sometimes better, though A and B tie in the left column.

Sources

About this calculator

In game theory, a strategy is dominant if it gives a player a payoff at least as good as their alternative strategy no matter what the opponent does. For a 2×2 game, this calculator compares the row player's payoffs for each of their two strategies against both possible moves by the column player: if one row strategy yields a payoff that is at least as high as the other in both columns and strictly higher in at least one, it dominates (weak dominance — ties in one column are allowed) and a rational player should choose it. If the two rows tie in both columns, or each wins in one column, neither is reported as dominant.

Economists, game theorists, and students use dominant strategy analysis as the first and simplest step in solving a game, because a dominant strategy lets a player ignore what the opponent might do entirely and removes a layer of strategic uncertainty. It's the foundation for concepts like the Prisoner's Dilemma, where each player has a dominant strategy that, followed by both, leads to a worse joint outcome than if they'd cooperated — and it's also the first check performed before searching for a more general Nash equilibrium in games without a dominant strategy.

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Comments (1)

  • Editorial team

    The tool uses only the row player's payoffs and treats a tie as acceptable, so strategy A beats B even when one column is equal and the other is better. To test the other player, rewrite the game from their side: their strategies as rows, your player's moves as columns, their payoffs in the cells. A result of None only means neither row wins in every column. What game are you analysing?

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