Generalized Secretary Optimization Problem
Let's assume the first strategy is the best until someone comes up with a better one, ok?

So we set a threshold for value (between 0 and v). If the value of the candidate is higher than the threshold, try to hire that candidate. Otherwise, interview the next candidate. If we interview several candidates in a row whose value is below the threshold, decrease the threshold until future candidates are likely to have a higher value. If d is low and the candidates decline offers, lower the threshold further. 

A few points to determine: the first threshold for value. It's probably ok to wait a few days and just interview candidates so we can see what kind of values they have. Then set a threshold so that 50% (or 20% or 80% or whatever%) of the candidates have higher values. 

Another point to determine: when we fail to hire a secretary, how frequently and how much should we lower the threshold.

If v is unknown, we obviously have to observe a few values before making good guesses for a good threshold.

If d is unknown, we'll have to try to hire a few candidates before tuning the algorithm.

What was not mentioned in the question: 


How long does it take for the candidate to accept or decline the job offer? 
Is the game over when the first candidate accepts the offer?
Can you play the game n times?


If you can't choose the candidates for the interview it seems like winning this game is a matter of coincidence but I might be wrong.