Calculator
Enter payoffs as ordered pairs: first is Player A, second is Player B.
Example data table
This example is preloaded by the “Load example” button.
| Player A \ Player B | Cooperate | Defect |
|---|---|---|
| Cooperate | (-1, -1) | (-3, 0) |
| Defect | (0, -3) | (-2, -2) |
Formula used
How to use this calculator
- Select matrix size from 2 to 4 for both players.
- Enter strategy names for rows and columns.
- Fill payoffs for each cell as A and B values.
- Set mixed probabilities p and q as any nonnegative numbers.
- Press Calculate Payoffs to view results above.
- Use CSV or PDF buttons to download the computed report.
FAQs
1) What does a payoff matrix represent?
A payoff matrix lists outcomes for every pair of strategies. Each cell shows Player A’s payoff and Player B’s payoff for that strategy combination.
2) How are mixed strategies handled here?
You enter probabilities for each strategy. The calculator normalizes them so they sum to one, then computes expected payoffs using weighted averages over all cells.
3) What is a best response?
A best response is a strategy that maximizes a player’s expected payoff against the opponent’s fixed strategy or mixed distribution.
4) What is a pure Nash equilibrium?
A pure Nash equilibrium is a cell where neither player can improve by changing strategies alone. It is a mutual best response in the table.
5) Why might there be no pure equilibrium?
Some games only have mixed-strategy equilibria. In those cases, no single cell satisfies mutual best-response conditions, even though an equilibrium can still exist.
6) What are dominated strategies?
A strategy is strictly dominated if another strategy always yields a higher payoff, regardless of the opponent’s choice. Dominated strategies can often be removed to simplify analysis.
7) Can I use this for non-zero-sum games?
Yes. Enter any payoffs for both players. The tool computes expected outcomes and pure equilibria without requiring payoffs to sum to zero.