Jill and John independently and simultaneously choose one of two actions, $[2\mathrm{.}5]$

A and B$.$ Choosing B guarantees a payoff of $1$ regardless of what

the other agent does. Choosing A brings a less certain outcome: if the

opponent chooses A as well, the payoff is $20,$ but if the opponent chooses

B then the payoff is zero. Which statement is true?

$($a$)$ Jill chooses A and John chooses A is the only Nash equilibrium.

$($b$)$ Jill chooses A and John chooses B is the only Nash equilibrium.

$($c$)$ Jill chooses B and John chooses A is the only Nash equilibrium.

$($d$)$ Jill chooses B and John chooses B is the only Nash equilibrium.

$($e$)$ Configurations in $($a$)$ and $($d$)$ are both Nash equilibria.