How to handle call for offer deadline?

[Amy A.]

I'm looking at a multi-family in a situation that I've never encountered before.  There is no asking price and there is a call-for-offers deadline.  The property is worth over $1M, but I have no idea what the seller is hoping to get.  It doesn't really matter anyway, since I know what it's worth to me.  

Usually, when I want to make an offer there is a sense of urgency.  In this case, I'm afraid that if I offer too early that he will shop my offer.  Should I wait until the deadline?   Do aggressive buyers ever demand a response to an offer immediately, call-to-offer deadlines be damned?

I really don't care too much if I get this property, but don't want to kick myself if I find out later that it was a good deal.

Is this a strategy often taken by sellers who are very motivated and will sell to the highest offer, or by those who don't care if it sells and are just fishing?