Interesting--I've interpreted your question somewhat differently than those answering below.
As I read your question, if all the offers are in the "same ball park," how long (how many offers) will it take until the owner realizes what the market value is? This situation sometimes comes up when an owner is convinced that his property is worth more than the Realtor is suggestion.
So, hypothetically, let's say the house is worth $410,000, according to the comps. The Realtor suggests putting it on the market at $419,000, to allow for a little wiggle room. The owner, however, is convinced that the house is worth $449,000, and the Realtor reluctantly agrees to put it on at that price, but that the price will drop if there's insufficient activity or interest.
So, if I understand your question, some offers do come in. But they're at, say, $410,000, $399,000, and $418,000. How many such offers does it take for the owner to realize the market value?
I'd say 2-4. The reaction to the first one is probably, "Oh, that's just an investor lowball." Second one might be, "Well, I guess they're looking for a bargain. But after a few more, most owners are going to realize that the market is speaking loud and clear to them.
Just my opinion. Hope that helps.