| Exam Board | OCR |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Dynamic Programming |
| Type | Zero-sum game optimal mixed strategy |
| Difficulty | Standard +0.3 This is a standard D2 game theory question requiring graphical representation of expected payoffs and finding optimal mixed strategies. While it involves multiple steps (plotting lines, finding intersection, solving simultaneous equations), the techniques are routine and well-practiced. The 2×3 matrix is straightforward, and the graphical method is a textbook procedure that students drill extensively in D2. |
| 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 |
2. 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{OCR D2 Q2 [8]}}