$(+9)$ Nature designates player $1$ as type $s$ or type $t,$ with equal probability. Observing her type, Player $1$ then takes action $a$ or $b.$ Observing Player $1\text{'}$s action but not Player $1\text{'}$s type, Player $2$ then chooses $x$ or $y.$ Payoffs for both players are given in the following table.

$\backslash$table$[[s,a,x,s,a,y,s,b,x,s,b,y,t,a,x,t,a,y,t,b,x,t,b,y$