3 In the pay-off matrix below, the entry in each cell is of the form \(( r , c )\), where \(r\) is the pay-off for the player on rows and \(c\) is the pay-off for the player on columns when they play that cell.
| P | Q | R |
| X | \(( 1,4 )\) | \(( 5,3 )\) | \(( 2,6 )\) |
| Y | \(( 5,2 )\) | \(( 1,3 )\) | \(( 0,1 )\) |
| Z | \(( 4,3 )\) | \(( 3,1 )\) | \(( 2,1 )\) |
- Show that the play-safe strategy for the player on columns is P .
- Demonstrate that the game is not stable.
The pay-off for the cell in row Y , column P is changed from \(( 5,2 )\) to \(( y , p )\), where \(y\) and \(p\) are real numbers.
- What is the largest set of values \(A\), so that if \(y \in A\) then row Y is dominated by another row?
- Explain why column P can never be redundant because of dominance.