| Exam Board | Edexcel |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2007 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Groups |
| Difficulty | Moderate -0.5 This is a standard two-person zero-sum game theory problem requiring checking for saddle points and then applying the simplex method or graphical solution for mixed strategies. While it involves multiple steps and calculation, it follows a well-defined algorithmic procedure taught in Decision Mathematics with no novel insight required, making it slightly easier than average A-level difficulty. |
| Spec | 7.08a Pay-off matrix: zero-sum games7.08c Pure strategies: play-safe strategies and stable solutions7.08e Mixed strategies: optimal strategy using equations or graphical method |
| H plays 1 | H plays 2 | H plays 3 | |
| D plays 1 | 2 | - 1 | 3 |
| D plays 2 | - 3 | 4 | - 4 |
2. Denis (D) and Hilary (H) play a two-person zero-sum game represented by the following pay-off matrix for Denis.
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
& H plays 1 & H plays 2 & H plays 3 \\
\hline
D plays 1 & 2 & - 1 & 3 \\
\hline
D plays 2 & - 3 & 4 & - 4 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Show that there is no stable solution to this game.
\item Find the best strategy for Denis and the value of the game to him.\\
(10) (Total 13 marks)
\end{enumerate}
\hfill \mbox{\textit{Edexcel D2 2007 Q2 [13]}}