once it happened worse to me, I specified my minimum acceptable price at the first contact, went trough three interviews, then they offered 87% of what I asked.
This works really well with a liquid market. It can be harder for people who are talented in specialized professions. My wife, for instance, is highly skilled in a very specialized skillset, but it's academic, and jobs that match her skills come up a few times a year in the whole state. Even though the applicant pool is small, the illiquidity means it's difficult to say you're going to someone else. Actually, I wonder to what extent markets with very specialized (and comparatively rare) talents are affected by this illiquidity as opposed to mere supply and demand?
You don't say what the minimum you will work for is, you tell them what your other offers are, then you have an auction and they have to bid up.