7 Each day Alix and Ben play a game. They each choose a card and use the table below to find the number of points they win. The table shows the cards available to each player. The entries in the cells are of the form ( \(a , b\) ), where \(a =\) points won by Alix and \(b =\) points won be Ben. Each is trying to maximise the points they win.
\begin{table}[h]
\captionsetup{labelformat=empty}
\caption{Ben}
| | Card X | Card Y | Card Z |
| Card P | \(( 4,4 )\) | \(( 5,9 )\) | \(( 1,7 )\) |
| \multirow[t]{2}{*}{Alix} | Card Q | \(( 3,5 )\) | \(( 4,1 )\) | \(( 8,2 )\) |
| Card R | \(( x , y )\) | \(( 2,2 )\) | \(( 9,4 )\) |
\end{table}
- Explain why the table cannot be reduced through dominance no matter what values \(x\) and \(y\) have.
- Show that the game is not stable no matter what values \(x\) and \(y\) have.
- Find the Nash equilibrium solutions for the various values that \(x\) and \(y\) can have.
\section*{OCR}
\section*{Oxford Cambridge and RSA}