Mixed strategies: the graphical methodEdexcel A-Level Further Maths: Mind map

Exam questions on Mixed strategies: the graphical method

1. Rose and Colin play a zero-sum game with Rose's pay-off matrix $\begin{pmatrix} 3 & -1 \\ -2 & 4 \end{pmatrix}$, where Rose chooses the rows. Rose plays row 1 with probability $p$ and row 2 with probability $1-p$.
   Find Colin's optimal strategy.2 marks
2. Rose and Colin play a zero-sum game with Rose's pay-off matrix $\begin{pmatrix} 2 & -1 & 4 \\ -3 & 3 & -2 \end{pmatrix}$, where Rose chooses the rows. Rose plays row 1 with probability $p$ and row 2 with probability $1-p$.
   Find Colin's optimal strategy.2 marks
3. A zero-sum game has Rose's pay-off matrix $\begin{pmatrix} 4 & -1 \\ 1 & 3 \\ -2 & 5 \end{pmatrix}$, where Rose chooses the rows. Colin plays column 1 with probability $q$ and column 2 with probability $1-q$.
   Find Colin's optimal strategy.3 marks