3 Two people, Rob and Con, play a zero-sum game.
The game is represented by the following pay-off matrix for Rob.
| \multirow{5}{*}{Rob} | Con |
| Strategy | \(\mathrm { C } _ { 1 }\) | \(\mathbf { C } _ { \mathbf { 2 } }\) | \(\mathrm { C } _ { 3 }\) |
| \(\mathbf { R } _ { \mathbf { 1 } }\) | -2 | 5 | 3 |
| \(\mathbf { R } _ { \mathbf { 2 } }\) | 3 | -3 | -1 |
| \(\mathbf { R } _ { \mathbf { 3 } }\) | -3 | 3 | 2 |
- Explain what is meant by the term 'zero-sum game'.
- Show that this game has no stable solution.
- Explain why Rob should never play strategy \(R _ { 3 }\).
- Find the optimal mixed strategy for Rob.
- Find the value of the game.