2. Rani and Greg play a zero-sum game. The pay-off matrix shows the number of points that Rani scores for each combination of strategies.
| Greg plays 1 | Greg plays 2 | Greg plays 3 |
| Rani plays 1 | - 3 | 1 | 2 |
| Rani plays 2 | 0 | 2 | 1 |
| Rani plays 3 | 2 | 4 | - 5 |
- Explain what the term 'zero-sum game' means.
- State the number of points that Greg scores if he plays his strategy 3 and Rani plays her strategy 3.
- Verify that there is no stable solution to this game.
- Reduce the game so that Greg has only two possible strategies. Write down the reduced pay-off matrix for Greg.
- Find the best strategy for Greg and the value of the game to him.