| Exam Board | OCR |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Dynamic Programming |
| Type | Zero-sum game dominance reduction |
| Difficulty | Moderate -0.3 This is a standard textbook exercise in game theory requiring systematic application of dominance rules followed by solving a 2×2 game. While it involves multiple steps, each step follows a well-defined algorithm taught in D2 with no novel insight required—slightly easier than average due to its procedural nature. |
| 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 method7.08f Mixed strategies via LP: reformulate as linear programming problem |
| \cline { 3 - 5 } \multicolumn{2}{c|}{} | \(B\) | |||
| \cline { 2 - 5 } \multicolumn{2}{c|}{} | I | II | III | |
| \multirow{3}{*}{\(A\)} | I | 3 | 5 | - 2 |
| \cline { 2 - 5 } | II | 7 | \({ } ^ { - } 4\) | - 1 |
| \cline { 2 - 5 } | III | 9 | \({ } ^ { - } 4\) | 8 |
2. The payoff matrix for player $A$ in a two-person zero-sum game is shown below.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\cline { 3 - 5 }
\multicolumn{2}{c|}{} & \multicolumn{3}{|c|}{$B$} \\
\cline { 2 - 5 }
\multicolumn{2}{c|}{} & I & II & III \\
\hline
\multirow{3}{*}{$A$} & I & 3 & 5 & - 2 \\
\cline { 2 - 5 }
& II & 7 & ${ } ^ { - } 4$ & - 1 \\
\cline { 2 - 5 }
& III & 9 & ${ } ^ { - } 4$ & 8 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Applying the dominance rule, explain, with justification, which strategy can be ignored by
\begin{enumerate}[label=(\roman*)]
\item player $A$,
\item player $B$.
\end{enumerate}\item For the reduced table, find the optimal strategy for
\begin{enumerate}[label=(\roman*)]
\item player $A$,
\item player $B$.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{OCR D2 Q2 [9]}}