| Exam Board | Edexcel |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2002 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Groups |
| Difficulty | Moderate -0.5 This is a standard game theory question requiring dominance reduction and solving a 2×2 zero-sum game using mixed strategies. While it involves multiple steps, the techniques are routine for Further Maths students: identifying dominated strategies, setting up probability equations, and solving for optimal mixed strategies. The conceptual difficulty is moderate but the procedures are well-practiced, making it slightly easier than average. |
| Spec | 7.08a Pay-off matrix: zero-sum games7.08b Dominance: reduce pay-off matrix7.08c Pure strategies: play-safe strategies and stable solutions7.08d Nash equilibrium: identification and interpretation7.08e Mixed strategies: optimal strategy using equations or graphical method |
4. Andrew ( $A$ ) and Barbara ( $B$ ) play a zero-sum game. This game is represented by the following payoff matrix for Andrew.
$$A \left( \begin{array} { c c c }
& B & \\
3 & 5 & 4 \\
1 & 4 & 2 \\
6 & 3 & 7
\end{array} \right)$$
\begin{enumerate}[label=(\alph*)]
\item Explain why this matrix may be reduced to
$$\left( \begin{array} { l l }
3 & 5 \\
6 & 3
\end{array} \right)$$
\item Hence find the best strategy for each player and the value of the game.\\
(8)
\end{enumerate}
\hfill \mbox{\textit{Edexcel D2 2002 Q4 [8]}}