The key to buying a property is often the negotiating process. Whether you are the seller or the buyer, it is helpful to have realistic expectations and know how to be thoughtful about the process. Every buyer and seller is different. It is considered a given that the buyer wants to get the lowest price possible and the seller, the highest, but the process is never as simple as that.
The seller should be interested in the "best" offer, that may or may not be the highest price. Many factors are involved: whether the buyer needs to sell something to buy, how much the buyer can put down, and in a coop situation, what are the buyer's assets after the downpayment. A smart seller goes through this process carefully with their broker. Many years ago I sold an apartment in Park Slope, where the previous broker had failed to go over the financials of his buyer. It was a relatively tough coop board and the buyer was turned down and the sellers lost a downpayment on a house. A very costly proposition. I vetted the next buyer carefully, coached him for the interview and the sale went well. Given a somewhat more difficult financing environment, these issues have become more important. A good broker advises his seller well and does his or her homework on the prospective buyer.
My advice for buyers is don't be too rigid. Yes, you want the best price, but with interest rates very low a small difference in the purchase price will not affect your wallet that adversely. If you find the home you want, be it a coop, condo or house, be willing to step up and do what you need to, as long it makes financial sense.
A good broker will guide the buyer and the seller through the process carefully, providing as much information as possible. Getting the best information possible makes the buyer and seller able to make good decisions. Make sure you work with a broker who is responsive and thoughtful.