| Exam Board | Edexcel |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Dynamic Programming |
| Type | Zero-sum game optimal mixed strategy |
| Difficulty | Moderate -0.3 This is a standard D2 game theory question requiring routine application of the minimax theorem and mixed strategy formulas. While it involves multiple steps (checking for saddle point, calculating optimal mixed strategies using the standard 2×2 formulas, finding game value), these are all textbook procedures with no novel problem-solving required. The calculations are straightforward arithmetic, making it slightly easier than an average A-level question. |
| Spec | 7.08a Pay-off matrix: zero-sum games7.08c Pure strategies: play-safe strategies and stable solutions7.08e Mixed strategies: optimal strategy using equations or graphical method |
| Y | |||
| \(Y_1\) | \(Y_2\) | ||
| \multirow{2}{*}{X} | \(X_1\) | \(-2\) | 4 |
| \(X_2\) | 6 | \(-1\) | |
The payoff matrix for player X in a two-person zero-sum game is shown below.
\begin{tabular}{c|cc}
& \multicolumn{2}{c}{Y} \\
& $Y_1$ & $Y_2$ \\
\hline
\multirow{2}{*}{X} & $X_1$ & $-2$ & 4 \\
& $X_2$ & 6 & $-1$ \\
\end{tabular}
\begin{enumerate}[label=(\alph*)]
\item Explain why the game does not have a saddle point. [3 marks]
\item Find the optimal strategy for
\begin{enumerate}[label=(\roman*)]
\item player X, [8 marks]
\item player Y.
\end{enumerate}
\item Find the value of the game. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel D2 Q6 [13]}}