- The payoff matrix for player \(A\) in a two-person zero-sum game with value \(V\) is shown below.
| \cline { 3 - 5 }
\multicolumn{2}{c|}{} | \(B\) |
| \cline { 2 - 5 }
\multicolumn{2}{c|}{} | I | II | III |
| \multirow{3}{*}{\(A\)} | I | 6 | - 4 | - 1 |
| \cline { 2 - 5 } | II | - 2 | 5 | 3 |
| \cline { 2 - 5 } | III | 5 | 1 | - 3 |
Formulate this information as a linear programming problem, the solution to which will give the optimal strategy for player \(B\).
- Rewrite the matrix as necessary and state the new value of the game, \(v\), in terms of \(V\).
- Define your decision variables.
- Write down the objective function in terms of your decision variables.
- Write down the constraints.