Dominant Strategy Finder

Example data table

This 2×2 example has dominant strategies for both players.

Interpretation: “Defect” strictly dominates “Cooperate” for both players because it yields higher payoffs against every opponent choice.

Formula used

Let Player A payoffs be u_A(i,j) and Player B payoffs be u_B(i,j).

• A strict dominance: Strategy i strictly dominates k if for every column j, u_A(i,j) > u_A(k,j).
• A weak dominance: Strategy i weakly dominates k if for every j, u_A(i,j) ≥ u_A(k,j) and for some j, it is strictly greater.
• B strict/weak dominance: Same logic across columns using u_B(i,j) while holding rows fixed.
• Dominant strategy: A strategy that dominates every other strategy of the same player.

How to use this calculator

1. Select the number of strategies for each player.
2. Optionally name strategies using comma-separated labels.
3. Enter each outcome payoff as A and B values.
4. Click Find dominant strategies to compute results.
5. Review strict, weak, pairwise, and dominated strategy lists.
6. Use CSV or PDF downloads to save your analysis.

Market framing through payoff matrices

A payoff matrix converts a strategic situation into numbers that can be tested. For an m×n game, you enter 2mn payoffs. The tool compares each A row across all B columns, then each B column across all A rows, highlighting dominance patterns that would be hard to see by inspection. Because inputs accept decimals, you can model probabilities, costs, or utilities on a common scale; rerun with alternative payoffs to test sensitivity before committing resources in real planning contexts.

Strict dominance as a filtering rule

A strategy is strictly dominant when every outcome against the opponent’s options yields a higher payoff. In data terms, row i strictly dominates row k when uA(i,j) > uA(k,j) for every column j. This guarantees the dominated strategy is never optimal, so it can be removed confidently.

Weak dominance and practical tie handling

Weak dominance allows ties while requiring at least one strict improvement. This matters in datasets with equal outcomes, discounts, or capped utilities. The calculator flags weakly dominated strategies, but you should interpret them carefully because removing weakly dominated options can change the set of equilibria in some games.

Interpreting pairwise dominance outputs

The pairwise list acts like an audit trail: it shows which strategy beats which alternative. If multiple strategies dominate the same target, the target is robustly dominated. If dominance chains appear, you can see a natural elimination order. Use the dominated-strategy summary to focus on the smallest relevant subset.

Using graphs to spot structure faster

Heatmaps visualize payoff gradients across the table. A rising band in the A heatmap often indicates a strong row candidate, while a rising band in the B heatmap indicates a strong column candidate. Large flat regions signal many ties, which increases the likelihood of weak dominance rather than strict dominance.

Exporting results for decisions and reports

CSV export captures the full matrix plus the computed dominance summary for spreadsheet review. PDF export is suited to sharing with teams, instructors, or clients. When documenting a decision, attach the matrix, note any strictly dominant strategies found, and record why weak dominance was accepted or rejected. For 8×8 inputs, comparisons scale roughly with m²n + n²m.

FAQs

1) What does “dominant strategy” mean here?

Your strategy is dominant if it performs at least as well as every other option against all opponent choices, and better in at least one case for weak dominance, or in every case for strict dominance.

2) Can a game have multiple dominant strategies?

Yes. If two strategies tie in every outcome and both weakly dominate all others, you may see multiple weakly dominant strategies. Strictly dominant strategies are rarer, but multiple can occur with identical payoff rows or columns.

3) Why do I see “dominated” but no “dominant” strategy?

A strategy can be dominated without any single strategy dominating all alternatives. Dominance is a global condition; dominated lists are pairwise. This often happens in rock–paper–scissors style games or when payoffs cross.

4) Do decimals change the dominance test?

No. The comparison uses standard greater-than and greater-or-equal checks on your numeric inputs. Decimals simply let you model utilities, costs, or expected values with more precision.

5) Is this the same as finding Nash equilibrium?

No. Dominance is about guaranteed payoff comparisons across all opponent actions. Nash equilibrium requires mutual best responses. A game can have no dominant strategies and still have equilibria, or have dominant strategies that simplify equilibrium finding.

6) What matrix size works best?

The tool supports 2 to 8 strategies per player for clarity and export readability. For larger games, consider reducing the strategy set first or analyzing subsets, then re-entering a smaller matrix for dominance screening.