4. Eugene and Stephen play a zero-sum game. The pay-off matrix shows the number of points that Eugene scores for each combination of strategies.
| Stephen plays 1 | Stephen plays 2 | Stephen plays 3 |
| Eugene plays 1 | 4 | 5 | 0 |
| Eugene plays 2 | -2 | 1 | 1 |
| Eugene plays 3 | -3 | -4 | 3 |
- Find the play-safe strategies for each of Eugene and Stephen, and hence show that this zero-sum game does not have a stable solution.
- Suppose that Eugene knows that Stephen will use his play-safe strategy. Explain why Eugene should change from his play-safe strategy. You should state as part of your answer which strategy Eugene should now play.
- Formulate the game as a linear programming problem for Stephen. Define your variables clearly. Write the constraints as equations.