Moderate -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.
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]}}