| Exam Board | AQA |
|---|---|
| Module | Further Paper 3 Discrete (Further Paper 3 Discrete) |
| Year | 2023 |
| Session | June |
| Marks | 1 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Dynamic Programming |
| Type | Zero-sum game dominance reduction |
| Difficulty | Moderate -0.5 This is a straightforward dominance check in a zero-sum game requiring students to compare rows to identify a dominated strategy. While it's a Further Maths topic (making it inherently more specialized), the mechanical process of comparing each entry is routine and requires no problem-solving insight—just systematic checking of which strategy is dominated, making it easier than average A-level difficulty. |
| Spec | 7.08b Dominance: reduce pay-off matrix |
| \multirow{6}{*}{Jonathan} | Hoshi | |||
| Strategy | \(\mathbf { H } _ { \mathbf { 1 } }\) | \(\mathbf { H } _ { \mathbf { 2 } }\) | \(\mathbf { H } _ { \mathbf { 3 } }\) | |
| \(\mathbf { J } _ { \mathbf { 1 } }\) | -2 | 3 | 2 | |
| \(\mathbf { J } _ { \mathbf { 2 } }\) | 3 | 2 | 0 | |
| \(\mathbf { J } _ { \mathbf { 3 } }\) | 4 | -1 | 3 | |
| \(\mathbf { J } _ { \mathbf { 4 } }\) | 3 | 1 | 0 | |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(J_4\) | B1 | Circles correct answer |
| Total: 1 |
## Question 2:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $J_4$ | B1 | Circles correct answer |
| **Total: 1** | | |
---2 Jonathan and Hoshi play a zero-sum game.\\
The game is represented by the following pay-off matrix for Jonathan.
\begin{center}
\begin{tabular}{|l|l|l|l|l|}
\hline
\multirow{6}{*}{Jonathan} & \multicolumn{4}{|c|}{Hoshi} \\
\hline
& Strategy & $\mathbf { H } _ { \mathbf { 1 } }$ & $\mathbf { H } _ { \mathbf { 2 } }$ & $\mathbf { H } _ { \mathbf { 3 } }$ \\
\hline
& $\mathbf { J } _ { \mathbf { 1 } }$ & -2 & 3 & 2 \\
\hline
& $\mathbf { J } _ { \mathbf { 2 } }$ & 3 & 2 & 0 \\
\hline
& $\mathbf { J } _ { \mathbf { 3 } }$ & 4 & -1 & 3 \\
\hline
& $\mathbf { J } _ { \mathbf { 4 } }$ & 3 & 1 & 0 \\
\hline
\end{tabular}
\end{center}
The game does not have a stable solution.\\
Which strategy should Jonathan never play?\\
Circle your answer.\\[0pt]
[1 mark]\\
$\mathbf { J } _ { \mathbf { 1 } }$\\
$\mathbf { J } _ { \mathbf { 2 } }$\\
$\mathbf { J } _ { \mathbf { 3 } }$\\
$\mathbf { J } _ { \mathbf { 4 } }$
\hfill \mbox{\textit{AQA Further Paper 3 Discrete 2023 Q2 [1]}}