| Exam Board | Edexcel |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Dynamic Programming |
| Type | Zero-sum game dominance reduction |
| Difficulty | Moderate -0.3 This is a standard D2 game theory question requiring dominance reduction and mixed strategy calculation. While it involves multiple steps (identifying dominated strategies, setting up equations for optimal mixed strategies), these are routine algorithmic procedures taught directly in the syllabus with minimal conceptual challenge or novel insight required. |
| Spec | 7.08b Dominance: reduce pay-off matrix7.08e Mixed strategies: optimal strategy using equations or graphical method |
Andrew ($A$) and Barbara ($B$) play a zero-sum game. This game is represented by the following pay-off matrix for Andrew.
$$A \begin{pmatrix} 3 & 5 & 4 \\ 1 & 4 & 2 \\ 6 & 3 & 7 \end{pmatrix}$$
\begin{enumerate}[label=(\alph*)]
\item Explain why this matrix may be reduced to
$$\begin{pmatrix} 3 & 5 \\ 6 & 3 \end{pmatrix}$$ [8]
\item Hence find the best strategy for each player and the value of the game.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D2 Q4 [8]}}