| Exam Board | OCR |
|---|---|
| Module | FD1 AS (Further Decision 1 AS) |
| Year | 2018 |
| Session | March |
| Marks | 9 |
| Topic | Dynamic Programming |
| Type | Zero-sum game optimal mixed strategy |
| Difficulty | Standard +0.3 This is a standard textbook exercise in zero-sum games requiring routine application of dominance arguments and graphical solution methods. While it involves multiple steps (reformulation, dominance elimination, graphical method), each step follows a well-practiced algorithm taught directly in FD1. The question requires no novel insight—students who have learned the techniques can apply them mechanically. Slightly easier than average A-level due to being a direct application of taught methods. |
| 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 |
| W | X | Y | Z | |
| P | 5 | 8 | 3 | 4 |
| Q | 4 | 2 | 7 | 5 |
| R | 2 | 1 | 5 | 3 |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | 8 | |
| 3 | 0 | 5 |
Question 3:
3 | 8
3 | 0 | 53 Lee and Maria are playing a strategy game. The tables below show the points scored by Lee and the points scored by Maria for each combination of strategies.
Points scored by Lee
Lee's choice
\begin{table}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Maria's choice}
\begin{tabular}{ c | c | c | c | c }
& W & X & Y & Z \\
\hline
P & 5 & 8 & 3 & 4 \\
\hline
Q & 4 & 2 & 7 & 5 \\
\hline
R & 2 & 1 & 5 & 3 \\
\hline
\end{tabular}
\end{center}
\end{table}
Points scored by Maria
Lee's choice\\
\includegraphics[max width=\textwidth, alt={}, center]{a51b112d-1f3f-4214-94c1-8b9cd7eb831c-3_335_481_392_1139}\\
(i) Show how this game can be reformulated as a zero-sum game.\\
(ii) By first using dominance to eliminate one of Lee's choices, use a graphical method to find the optimal mixed strategy for Lee.
\hfill \mbox{\textit{OCR FD1 AS 2018 Q3 [9]}}