| Exam Board | Edexcel |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2016 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear Programming |
| Type | Game theory LP formulation |
| Difficulty | Standard +0.8 This D2 question requires understanding game theory concepts (stable solutions, saddle points), formulating a mixed-strategy game as an LP with probability constraints, and setting up a simplex tableau. While methodical, it demands synthesis of multiple Decision Maths techniques beyond routine application, placing it moderately above average difficulty. |
| Spec | 7.08a Pay-off matrix: zero-sum games7.08f Mixed strategies via LP: reformulate as linear programming problem |
| B plays 1 | B plays 2 | B plays 3 | |
| A plays 1 | 5 | - 3 | 1 |
| A plays 2 | 2 | 5 | 0 |
| A plays 3 | - 4 | - 1 | 4 |
6. A two-person zero-sum game is represented by the following pay-off matrix for player A.
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
& B plays 1 & B plays 2 & B plays 3 \\
\hline
A plays 1 & 5 & - 3 & 1 \\
\hline
A plays 2 & 2 & 5 & 0 \\
\hline
A plays 3 & - 4 & - 1 & 4 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Verify that there is no stable solution to this game.
\item Formulate the game as a linear programming problem for player A. Define your variables clearly. Write the constraints as equations.
\item Write down an initial simplex tableau, making your variables clear.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D2 2016 Q6 [12]}}