code class$=$"asciimath"$>$There are two players: Q and J$.$Q can choose between two options: a and b$.$ J can choose between two options: c and d$.$J can be of two types: $\backslash$theta in$\{$l$,$h$\}$Q cannot see J $\text{'}$s type.l is p$.$ Payoffs are as follows: u$^($J$)(*,$c$|\backslash$theta $)=1$ for all $\backslash$theta and all actions of Q u$^($J$)(*,$d$|$l$)=0$ for all actions of Q u$^($J$)($a$,$d$|$h$)=2$ u$^($J$)($b$,$d$|$h$)=0$ u$^($Q$)(*,$c$|\backslash$theta $)=0$ for all $\backslash$theta and all actions of Q u$^($Q$)(*,$d$|$l$)=0$ for all actions of Q u$^($Q$)($a$,$d$|$h$)=1$ u$^($Q$)($b$,$d$|$h$)=02\mathrm{.}1$ Is $\text{'}$ J always plays c and Q plays b $\text{'}$ a Bayes Nash equi$-$ librium? $2\mathrm{.}2$ Assume that Q can observe the action of J before making her choice. Also, assume that if J plays c$,$ the game ends there. Is $\text{'}$ J always plays c and Q plays b and beliefs Pr$($h$|$d$)=0\text{'}$ a perfect Bayesian equi$-$ librium? $($it might help to write draw the extensive form representation of the game, but it is not strictly necessary$)$