Mixed strategies: the graphical method Quiz

1. Rose plays row 1 with probability $p$ in $\begin{pmatrix} 2 & 5 \\ 4 & 1 \end{pmatrix}$. What is her expected pay-off if Colin plays column 1?

• A. $2p+4$
• B. $4-2p$
• C. $2p-4$
• D. $6p$

2. In $\begin{pmatrix} 3 & 0 \\ 1 & 2 \end{pmatrix}$, Rose plays row 1 with probability $p$. Find her optimal $p$.

• A. $\frac12$
• B. $\frac13$
• C. $\frac14$
• D. $\frac34$

3. What is the value of the game in the previous question?

• A. $\frac32$
• B. $1$
• C. $2$
• D. $\frac14$

4. In the graphical method for a $2\times n$ game, Rose chooses $p$ to...

• A. make all lines equal
• B. minimise the highest line
• C. maximise the highest line
• D. maximise the lowest line

5. In an $n\times2$ game, Colin plays column 1 with probability $q$. He chooses $q$ to...

• A. maximise the lowest line
• B. minimise the highest of the lines
• C. make the lines parallel
• D. choose the steepest line