7. 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 |
| \(A\) plays 1 | 5 | 7 | 2 |
| \(A\) plays 2 | 3 | 8 | 4 |
| \(A\) plays 3 | 6 | 4 | 9 |
- Formulate the game as a linear programming problem for player \(A\), writing the constraints as equalities and clearly defining your variables.
- Explain why it is necessary to use the simplex algorithm to solve this game theory problem.
- Write down an initial simplex tableau making your variables clear.
- Perform two complete iterations of the simplex algorithm, indicating your pivots and stating the row operations that you use.
(8)
(Total 16 marks)