4 Two people, Roger and Corrie, play a zero-sum game.
The game is represented by the following pay-off matrix for Roger.
| Corrie | |
| \cline { 2 - 5 } | Strategy | \(\mathbf { C } _ { \mathbf { 1 } }\) | \(\mathbf { C } _ { \mathbf { 2 } }\) | \(\mathbf { C } _ { \mathbf { 3 } }\) |
| \cline { 2 - 5 }
Roger | \(\mathbf { R } _ { \mathbf { 1 } }\) | 7 | 3 | - 5 |
| \cline { 2 - 5 } | \(\mathbf { R } _ { \mathbf { 2 } }\) | - 2 | - 1 | 4 |
| \cline { 2 - 5 } | | | | |
| \cline { 2 - 5 } |
- Find the optimal mixed strategy for Roger.
- Show that the value of the game is \(\frac { 7 } { 13 }\).
- Given that the value of the game is \(\frac { 7 } { 13 }\), find the optimal mixed strategy for Corrie.
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