QUESTION $8$

The payoff matrix for a two$-$player normal form game is given below.

A

B

C

M

$\backslash$begin$\{$tabular$\}\{|$l$|$l$|$l$|\}$

$\backslash$hline $1,2$ & $4,5$ & $6,3\backslash \backslash$

$\backslash$hline $2,2$ & $5,1$ & $2,4\backslash \backslash$

$\backslash$hline $4,2$ & $1,5$ & $7,3\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

Denote the probability of playing $"$M$"$ for Player $1$ as $\backslash ($ p $\backslash )$ and the probability of playing $"$ B $"$ for Player $2$ as q $.$ At which value of $\backslash ($ q $\backslash )$ will Player $1$ be willing to mix between $\backslash ($ M $\backslash )$ and $\backslash ($ N $\backslash )?$

Write your answer as a decimal number with $2$ decimal places $($e$.$g$.0\mathrm{.}05)$