OCR D2 — Question 1 4 marks

Exam BoardOCR
ModuleD2 (Decision Mathematics 2)
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicDynamic Programming
TypeZero-sum game dominance reduction
DifficultyModerate -0.8 This is a standard D2 game theory question requiring routine application of the minimax theorem to find saddle points or mixed strategies. With 4 marks, it likely has a pure strategy solution (saddle point) found by checking row minima and column maxima, which is a mechanical procedure taught explicitly in the specification with minimal problem-solving required.
Spec7.08a Pay-off matrix: zero-sum games7.08c Pure strategies: play-safe strategies and stable solutions

The payoff matrix for player \(A\) in a two-person zero-sum game is shown below. \begin{array}{c|c|c|c|c} & & \multicolumn{3}{c}{B}
& & \text{I} & \text{II} & \text{III}
\hline \multirow{3}{*}{A} & \text{I} & -3 & 4 & 0
& \text{II} & 2 & 2 & 1
& \text{III} & 3 & -2 & -1
\end{array} Find the optimal strategy for each player and the value of the game. [4 marks]

The payoff matrix for player $A$ in a two-person zero-sum game is shown below.

\begin{array}{c|c|c|c|c}
 & & \multicolumn{3}{c}{B} \\
 & & \text{I} & \text{II} & \text{III} \\
\hline
\multirow{3}{*}{A} & \text{I} & -3 & 4 & 0 \\
 & \text{II} & 2 & 2 & 1 \\
 & \text{III} & 3 & -2 & -1 \\
\end{array}

Find the optimal strategy for each player and the value of the game. [4 marks]

\hfill \mbox{\textit{OCR D2  Q1 [4]}}