3. Haruki and Meera play a zero-sum game. The game is represented by the following pay-off matrix for Haruki.
| \multirow{2}{*}{} | Meera |
| | Option X | Option Y | Option Z |
| \multirow{4}{*}{Haruki} | Option A | 4 | -2 | -5 |
| Option B | 1 | 4 | -3 |
| Option C | -1 | 6 | 1 |
| Option D | -4 | 5 | 3 |
- Determine whether the game has a stable solution.
Option Y for Meera is now removed.
- Write down the reduced pay-off matrix for Meera.
- Given that Meera plays Option X with probability \(p\), determine her best strategy.
- State the value of the game to Haruki.
- State which option(s) Haruki should never play.
The number of points scored by Haruki when he plays Option C and Meera plays Option X changes from - 1 to \(k\)
Given that the value of the game is now the same for both players,
- determine the value of \(k\). You must make your method and working clear.