2. A two-person zero-sum game is represented by the following pay-off matrix for player A.
| B plays 1 | B plays 2 | B plays 3 | B plays 4 |
| A plays 1 | -3 | 2 | 5 | -1 |
| A plays 2 | -5 | 3 | 1 | -1 |
| A plays 3 | -2 | 5 | 4 | 2 |
| A plays 4 | 2 | -3 | -1 | 4 |
- Identify the play safe strategies for each player.
- State, giving a reason, whether there is a stable solution to this game.
- Explain why the game above can be reduced to the following \(3 \times 3\) game.
- Formulate the \(3 \times 3\) game as a linear programming problem for player A, defining your variables clearly and writing the constraints as inequalities.