In the standard Secretary Problem, the goal is to hire the best secretary from a list of candidates. I've recently witnessed a failed hiring attempt for a needed position and it inspired a similar game:
The goal is to maximize the net score. Each candidate has a value that (if hired) would be added to the score. And each day that goes by without hiring a candidate costs the company 1 point of score. Starting score is 0.
Each day, the company either interviews a new candidate or attempts to hire a previously interviewed candidate. The value of the candidate is discovered during the interview and is uniformly distributed between $0$ and (known) $v$. There is an unlimited number of possible candidates to interview.
If the job is offered to a candidate, then the candidate will accept with a probability of $d^k$ for (known) constant $d$ and $k$ being the number of days since the candidate was interviewed. You may only attempt to hire a candidate once.
So the question is: what is the best strategy for this game given $v$ and $d$? Other natural questions: what is the best strategy if $v$ and/or $d$ are unknown?
Any insights, answers, or references to similar games would be appreciated.