6 The pay-off matrix for a game between two players, Sumi and Vlad, is shown below. If Sumi plays A and Vlad plays X then Sumi gets X points and Vlad gets 1 point.
Sumi
| Vlad | | |
| \cline { 2 - 4 }
\multicolumn{1}{c}{} | \(X\) | \(Y\) | \(Z\) |
| A | \(( x , 1 )\) | \(( 4 , - 2 )\) | \(( 2,0 )\) |
| B | \(( 3 , - 1 )\) | \(( 6 , - 4 )\) | \(( - 1,3 )\) |
You are given that cell ( \(\mathrm { A } , \mathrm { X }\) ) is a Nash Equilibrium solution.
- Find the range of possible values of X .
- Explain what the statement 'cell (A, X) is a Nash Equilibrium solution' means for each player.
- Find a cell where each player gets their maximin pay-off.
Suppose, instead, that the game can be converted to a zero-sum game.
- Determine the optimal strategy for Sumi for the zero-sum game.
- Record the pay-offs for Sumi when the game is converted to a zero-sum game.
- Describe how Sumi should play using this strategy.