Zero-sum game dominance reduction

A question is this type if and only if it asks to reduce a pay-off matrix by identifying and eliminating dominated strategies for either player.

4 questions · Moderate -0.5

7.08b Dominance: reduce pay-off matrix
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OCR D2 Q2
9 marks Moderate -0.3
2. The payoff matrix for player \(A\) in a two-person zero-sum game is shown below.
\cline { 3 - 5 } \multicolumn{2}{c|}{}\(B\)
\cline { 2 - 5 } \multicolumn{2}{c|}{}IIIIII
\multirow{3}{*}{\(A\)}I35- 2
\cline { 2 - 5 }II7\({ } ^ { - } 4\)- 1
\cline { 2 - 5 }III9\({ } ^ { - } 4\)8
  1. Applying the dominance rule, explain, with justification, which strategy can be ignored by
    1. player \(A\),
    2. player \(B\).
  2. For the reduced table, find the optimal strategy for
    1. player \(A\),
    2. player \(B\).
AQA Further Paper 3 Discrete 2023 June Q2
1 marks Moderate -0.5
2 Jonathan and Hoshi play a zero-sum game.
The game is represented by the following pay-off matrix for Jonathan.
\multirow{6}{*}{Jonathan}Hoshi
Strategy\(\mathbf { H } _ { \mathbf { 1 } }\)\(\mathbf { H } _ { \mathbf { 2 } }\)\(\mathbf { H } _ { \mathbf { 3 } }\)
\(\mathbf { J } _ { \mathbf { 1 } }\)-232
\(\mathbf { J } _ { \mathbf { 2 } }\)320
\(\mathbf { J } _ { \mathbf { 3 } }\)4-13
\(\mathbf { J } _ { \mathbf { 4 } }\)310
The game does not have a stable solution.
Which strategy should Jonathan never play?
Circle your answer.
[0pt] [1 mark] \(\mathbf { J } _ { \mathbf { 1 } }\) \(\mathbf { J } _ { \mathbf { 2 } }\) \(\mathbf { J } _ { \mathbf { 3 } }\) \(\mathbf { J } _ { \mathbf { 4 } }\)
Edexcel D2 Q4
8 marks Moderate -0.3
Andrew (\(A\)) and Barbara (\(B\)) play a zero-sum game. This game is represented by the following pay-off matrix for Andrew. $$A \begin{pmatrix} 3 & 5 & 4 \\ 1 & 4 & 2 \\ 6 & 3 & 7 \end{pmatrix}$$
  1. Explain why this matrix may be reduced to $$\begin{pmatrix} 3 & 5 \\ 6 & 3 \end{pmatrix}$$ [8]
  2. Hence find the best strategy for each player and the value of the game.
OCR D2 Q1
4 marks Moderate -0.8
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]