Enter payoff matrix
Choose 2 to 4 strategies for each player. Enter Player A payoff and Player B payoff separately for every outcome.
Example data table
| Player A \ Player B | Advertise | Hold |
|---|---|---|
| Advertise | (4, 4) | (7, 2) |
| Hold | (2, 7) | (5, 5) |
This sample lets you test pure equilibria, best responses, and the 2x2 mixed strategy module in one quick run.
Formula used
Pure Nash condition: an outcome (i, j) is an equilibrium when Player A's payoff at row i is maximal in column j, and Player B's payoff at column j is maximal in row i.
Best response rule: choose the strategy that gives the highest payoff against the opponent's fixed move.
Maximin rule: for each strategy, take the minimum payoff. Then select the strategy with the largest minimum payoff.
2x2 mixed equilibrium: solve the indifference equations. If Player A plays row 1 with probability p and Player B plays column 1 with probability q, the solver finds p and q where both players are indifferent between their available strategies.
How to use this calculator
- Choose the number of strategies for both players.
- Name each strategy so the output stays readable.
- Enter payoffs for every outcome pair in the matrix.
- Click Solve equilibrium to generate results above the form.
- Review pure equilibria, best responses, dominance notes, and maximin values.
- If the game is 2x2, also review the mixed strategy output.
- Use CSV or PDF export to save the result summary.
Frequently asked questions
1. What does this solver calculate?
It identifies pure strategy Nash equilibria, highlights best responses, checks strict dominance, reports maximin strategies, and solves interior mixed equilibria for 2x2 games.
2. Can I use decimal payoffs?
Yes. The payoff inputs accept integers and decimals, so you can model utilities, profits, scores, or normalized values without changing the logic.
3. Why is there no mixed equilibrium result for some games?
The mixed solver is limited to 2x2 games. Even there, some matrices have no interior mixed solution because computed probabilities fall outside the zero to one interval.
4. Does no pure equilibrium mean the game is unsolved?
No. Some games have no pure equilibrium but still have a mixed equilibrium. That is why the calculator separately checks the 2x2 mixed case.
5. What is a best response?
A best response is the strategy that gives the highest payoff against a specific action chosen by the other player.
6. What do dominant and dominated strategies mean?
A strictly dominant strategy always pays more than every alternative. A strictly dominated strategy always pays less and can often be removed from strategic analysis.
7. What is included in the export files?
The exports save the visible result summary, including equilibrium findings, dominance notes, security values, and the best response map shown after solving.