5. 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 | - 2 | 1 | 3 | - 1 |
| A plays 2 | - 1 | 3 | 2 | 1 |
| A plays 3 | - 4 | 2 | 0 | - 1 |
| A plays 4 | 1 | - 2 | - 1 | 3 |
- Verify that there is no stable solution to this game.
- Explain why the \(4 \times 4\) game above may be reduced to the following \(3 \times 3\) game.
- Formulate the \(3 \times 3\) game as a linear programming problem for player A. Write the
constraints as inequalities. Define your variables clearly.