Pay-off matrix
A pay-off matrix shows the possible outcomes for each combination of strategies chosen by the players in a game.
Each cell represents the outcome for Player 1. In a zero sum game, the outcome for Player 2 is the negative of the outcome for Player 1.
Example pay-off matrix
| Player 2 plays C | Player 2 plays D | Player 2 plays E | |
|---|---|---|---|
| Player 1 plays A | 2 | -1 | 1 |
| Player 1 plays B | 1 | -2 | -3 |
Row and column minima
We can add the row and column minima to the pay-off matrix to help us analyse the game:
| Player 2 plays C | Player 2 plays D | Player 2 plays E | Row minima | |
|---|---|---|---|---|
| Player 1 plays A | 2 | -1 | 1 | -1 |
| Player 1 plays B | 1 | -2 | -3 | -3 |
| Column maxima | 2 | -1 | 1 |
- The row minima are the worst outcomes for Player 1 for each of their strategies.
- The column maxima are the best outcomes for Player 1 for each of Player 2’s strategies (so the worst outcomes for Player 2).