Dominance and mixed strategiesAQA A-Level Further Maths: Mind map

Exam questions on Dominance and mixed strategies

1. Rowan and Colin play a zero-sum game. The pay-off matrix for Rowan is $\begin{pmatrix} 3 & 2 & 4 \\ 1 & 5 & 2 \\ 4 & 3 & 5 \end{pmatrix}$. Rows are Rowan's strategies and columns are Colin's. Rowan wants to maximise his pay-off and Colin wants to minimise it.
   Explain why Colin will never play column 3.2 marks
2. Rowan and Colin play a zero-sum game with pay-off matrix for Rowan $\begin{pmatrix} 5 & 1 \\ 2 & 4 \end{pmatrix}$. The game has no stable solution. Rowan chooses row 1 with probability $p$ and row 2 with probability $1-p$, to maximise his smallest expected pay-off.
   Find Colin's optimal strategy.2 marks
3. Rowan and Colin play a zero-sum game with pay-off matrix for Rowan $\begin{pmatrix} 2 & 5 & 1 \\ 4 & 1 & 6 \end{pmatrix}$. The game has no stable solution. Rowan chooses row 1 with probability $p$ and row 2 with probability $1-p$. Colin has three strategies, columns 1, 2 and 3.
   Write down Rowan's expected pay-off, in terms of $p$, when Colin plays each of columns 1, 2 and 3.3 marks