Consider the Following Payoff Matrix That Shows the Outcomes for Two

Consider the following payoff matrix that shows the outcomes for two individuals, Aaron and Bob, as they try to decide whether or not to ask out the prettiest and smartest girl in school, Caroline. Caroline likes Aaron better than Bob, but will accept Bob's invitation if Aaron does not ask her out. Assuming that having your offer for a date accepted is the best possible outcome, being rejected is the worst, and having "nothing" happen is in the middle.
$\begin{array} { l } & \text {BOB }\\ \text {AARON }&\begin{array}{l|l|l|}&\text { Ask her out } & \text { Don't } \\\hline \text { Ask}&\text { A: Accepted } & \text { A: Accepted } \\\text { her out}&\text { B: Rejected } & \text { B: Nothing } \\\hline& \text { A: Nothing } & \text { A: Nothing } \\ \text {don't }&\text { B: Accepted } & \text { B: Nothing }\end{array}\end{array}$
What will each of the boys decide to do?