5. (a) In game theory, explain the circumstances under which column \(( x )\) dominates column \(( y )\) in a two-person zero-sum game.
Liz and Mark play a zero-sum game. This game is represented by the following pay-off matrix for Liz.
| Mark plays 1 | Mark plays 2 | Mark plays 3 |
| Liz plays 1 | 5 | 3 | 2 |
| Liz plays 2 | 4 | 5 | 6 |
| Liz plays 3 | 6 | 4 | 3 |
(b) Verify that there is no stable solution to this game.
(c) Find the best strategy for Liz and the value of the game to her.
The game now changes so that when Liz plays 1 and Mark plays 3 the pay-off to Liz changes from 2 to
4. All other pay-offs for this zero-sum game remain the same.
(d) Explain why a graphical approach is no longer possible and briefly describe the method Liz should use to determine her best strategy.
(2) (Total 16 marks)