5 In each turn of a game between two players they simultaneously each choose a strategy and then calculate the points won using the table below. They are each trying to maximise the number of points that they win.
In each cell the first value is the number of points won by player 1 and the second value is the number of points won by player 2 .
| \multirow{2}{*}{} | Player 2 |
| | X | Y | Z |
| \multirow{3}{*}{Player 1} | A | \(( 6,0 )\) | \(( 1,7 )\) | \(( 5,6 )\) |
| B | \(( 9,4 )\) | \(( 2,6 )\) | \(( 8,1 )\) |
| C | \(( 6,8 )\) | \(( 1,3 )\) | \(( 7,2 )\) |
- Find the play-safe strategy for each player.
- Explain why player 2 would never choose strategy Z .
- Find the Nash equilibrium solution(s) or show that there is no Nash equilibrium solution.
Player 2 chooses strategy X with probability \(p\) and strategy Y with probability \(1 - p\).
You are given that when player 1 chooses strategy A, the expected number of points won by each player is the same.
- Calculate the value of \(p\).
- Determine which player expects to win the greater number of points when player 1 chooses strategy B.