| Exam Board | Edexcel |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Groups |
| Difficulty | Easy -3.0 This question is completely misclassified - it's about game theory (Decision Mathematics), not group theory (Further Pure Mathematics). Even as a game theory question, it's a routine textbook exercise involving drawing payoff lines and finding intersections, requiring only mechanical application of standard algorithms with no mathematical depth or insight. |
| 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 |
| \cline { 3 - 5 } \multicolumn{2}{c|}{} | \(B\) | |||
| \cline { 3 - 5 } \multicolumn{2}{c|}{} | I | II | III | |
| \multirow{2}{*}{\(A\)} | I | 1 | - 1 | 2 |
| \cline { 2 - 5 } | II | 3 | 5 | - 1 |
Question 3:
**A**
- AD
- AE
- AF
**B**
- BD
- BE
- BF
**C**
- CD
- CE
- CF3. A two-person zero-sum game is represented by the payoff matrix for player $A$ shown below.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\cline { 3 - 5 }
\multicolumn{2}{c|}{} & \multicolumn{3}{|c|}{$B$} \\
\cline { 3 - 5 }
\multicolumn{2}{c|}{} & I & II & III \\
\hline
\multirow{2}{*}{$A$} & I & 1 & - 1 & 2 \\
\cline { 2 - 5 }
& II & 3 & 5 & - 1 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Represent the expected payoffs to $A$ against $B$ 's strategies graphically and hence determine which strategy is not worth considering for player $B$.
\item Find the best strategy for player $A$ and the value of the game.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D2 Q3 [9]}}