3. In your answer to this question you must show detailed reasoning.
A two-person zero-sum game is represented by the following pay-off matrix for player A.
| \cline { 2 - 3 }
\multicolumn{1}{c|}{} | B plays \(X\) | B plays \(Y\) |
| A plays \(Q\) | 4 | - 3 |
| A plays \(R\) | 2 | - 1 |
| A plays \(S\) | - 3 | 5 |
| A plays \(T\) | - 1 | 3 |
- Verify that there is no stable solution to this game.
Player B plays their option X with probability \(p\).
- Use a graphical method to find the optimal value of \(p\) and hence find the best strategy for player B.
- Find the value of the game to player A .
- Hence find the best strategy for player A .