3 Amir and Beth play a zero-sum game.
The table shows the pay-off for Amir for each combination of strategies, where these values are known.
\begin{table}[h]
\captionsetup{labelformat=empty}
\caption{Beth}
| | X | Y | Z |
| \cline { 3 - 5 }
Amir | P | 2 | - 3 | \(c\) |
| \cline { 3 - 5 } | Q | - 3 | \(b\) | 4 |
| \cline { 3 - 5 } | R | \(a\) | - 1 | - 2 |
| \cline { 3 - 5 } | | | | |
| \cline { 3 - 5 } |
\end{table}
You are given that \(\mathrm { a } < 0 < \mathrm { b } < \mathrm { c }\).
Amir's play-safe strategy is R.
- Determine the range of possible values of \(a\).
Beth's play-safe strategy is Y.
- Determine the range of possible values of \(b\).
- Determine whether or not the game is stable.