3 Two people, Roz and Colum, play a zero-sum game. The game is represented by the following pay-off matrix for Roz.
| Colum | |
| \cline { 2 - 5 } | Strategy | \(\mathbf { C } _ { \mathbf { 1 } }\) | \(\mathbf { C } _ { \mathbf { 2 } }\) | \(\mathbf { C } _ { \mathbf { 3 } }\) |
| \multirow{3}{*}{\(\operatorname { Roz }\)} | \(\mathbf { R } _ { \mathbf { 1 } }\) | - 2 | - 6 | - 1 |
| \cline { 2 - 5 } | \(\mathbf { R } _ { \mathbf { 2 } }\) | - 5 | 2 | - 6 |
| \cline { 2 - 5 } | \(\mathbf { R } _ { \mathbf { 3 } }\) | - 3 | 3 | - 4 |
- Explain what is meant by the term 'zero-sum game'.
- Determine the play-safe strategy for Colum, giving a reason for your answer.
- Show that the matrix can be reduced to a 2 by 3 matrix, giving the reason for deleting one of the rows.
- Hence find the optimal mixed strategy for Roz.