I got an offer for a postdoc in a great US university A. I am still waiting to hear from another postdoc position also in a great US university B. The search committee at university B mentioned that their decisions would be made by a deadline that is prior to the deadline I have to decide about university A's offer.
I know that the usual advice about Tenure Track positions is to inform all places you are still waiting to hear from, about the offer(s) one gets. It is often said that it can even help one's chances of receiving other offers.
What isn't clear to me is whether the same applies to postdocs. That is, strategically speaking, should I inform university B of the offer I received from university A in this particular postdoc case? I have the impression that for a postdoc, it may harm more than help the chances of getting an offer from university B (which would be my preferred place).
Note: my goal is not to enforce negotiations. Rather, it is to make sure that, if university B was to make me an offer, they indeed would let me know before I have to reply to A. Like I said, theoretically, by their informed schedule, that should happen - but I have rarely seen such job-search schedules be respected. On the other hand, my concern is that such an email informing B of A's offer may harm my chances of getting the offer from B. For example because they prefer to give to another candidate slightly below in their preference rank but with no second disputing offer. I know that in Tenure Track searches that would not be likely, I am not so sure about postdoc searches.