wilmott.com

Let B be big bank that wants to hire someone for a vacant position. There are N candidates. Assume that there exists a total order relation between candidates that model the bank's preferences (relying upon what you want), that is, the bank can always distinguish between 2 canditates and there is some kind of transition principle, that is if A > B and B > C then A>C. Let's cut on the details from now on.The bank is big, but not big enough to keep candidate wait, so that it has to tell them right after the interview if they hire them or not, and if not, this is irreversible. The order in which the candidates are interviewed is random.Question reads, 'What is the optimal strategy of the bank.'When N's big, can you give a thumb's rule that gives the number of candidate to be interviewed.nota bene: harder than other posts.

Otherwise known as the marriage problem... Here's the bank's optimal strategy if their goal is to maximize the likelihood of hiring the best candidate: When you're 1/e of the way through the sample you decide that the next candidate that's better than all the previous candidates is the one you're going to hire. Odds of hiring the best candidate = 1/e in the limit...

The marriage's lemma I know is from Gale and Shapley. I don't quite see how it comes in. Well, I see but we have to modify the problem.Edit: Apart from that, your answer sounds ok.

Yes, but can you show it on the back of an envelope

so, how do u do this problem? i'm totally stuck...

There is a nice discussion of this problem (also called "Secretary problem") athttp://www.math.uah.edu/stat/urn/Secretary.xhtmlFor N large, 1/e is indeed the right strategy.