The art of "splitting the difference" is still around but don't depend on it.  As a buyer you should realize that buying the right business often doesn't really cost any money.  A well-priced business with a good cash flow should pay itself off.  Do you want to play games and lose the purchase to some other offeror?  Do you want to win -- or appear to win?

Mr. Seller -- if you want to play tennis reserve a court.  Anytime you refuse an offer to purchase you have actually bought the business back at that price.  If you pass up a certain price offer and refuse a sale you lose the ability to control that amount of money.  It's like buying your business back, isn't it?