2 Two people, Rowena and Colin, play a zero-sum game.
The game is represented by the following pay-off matrix for Rowena.
| \multirow{5}{*}{Rowena} | Colin |
| Strategy | \(\mathrm { C } _ { 1 }\) | \(\mathbf { C } _ { \mathbf { 2 } }\) | \(\mathrm { C } _ { 3 }\) |
| \(\mathbf { R } _ { \mathbf { 1 } }\) | -4 | 5 | 4 |
| \(\mathbf { R } _ { \mathbf { 2 } }\) | 2 | -3 | -1 |
| \(\mathbf { R } _ { \mathbf { 3 } }\) | -5 | 4 | 3 |
- Explain what is meant by the term 'zero-sum game'.
- Determine the play-safe strategy for Colin, giving a reason for your answer.
- Explain why Rowena should never play strategy \(R _ { 3 }\).
- Find the optimal mixed strategy for Rowena.