3 Rebecca and Claire repeatedly play a zero-sum game in which they each have a choice of three strategies, \(X , Y\) and \(Z\).
The table shows the number of points Rebecca scores for each pair of strategies.
\begin{table}[h]
\captionsetup{labelformat=empty}
\caption{Claire}
| \(X\) | \(Y\) | \(Z\) | |
| \cline { 2 - 5 } | \(X\) | 5 | - 3 | 1 |
| \cline { 2 - 5 }
Rebecca | \(Y\) | 3 | 2 | - 2 |
| \cline { 2 - 5 } | \(Z\) | - 1 | 1 | 3 |
| \cline { 2 - 5 } | | | | |
| \cline { 2 - 5 } |
\end{table}
- If both players choose strategy \(X\), how many points will Claire score?
- Show that row \(X\) does not dominate row \(Y\) and that column \(Y\) does not dominate column \(Z\).
- Find the play-safe strategies. State which strategy is best for Claire if she knows that Rebecca will play safe.
- Explain why decreasing the value ' 5 ' when both players choose strategy \(X\) cannot alter the playsafe strategies.