Since all else equal the seller wants to get the highest price possible for the house, one obvious differentiator of buyers is the maximum they are willing to pay for the house. A factor related to this is the buyer's ability to obtain financing, which depends on income, credit rating, and tangible assets. Another important aspect is timing. When does the buyer want to close the deal (and then move in)? The nearer that is to when the seller wants to close, the better. Sellers also might be concerned about the likelihood that the buyer will walk away from the deal. Usually a buyer is required to put up "earnest money" once a tentative agreement has been reached. In a seller's market (excess demand) a buyer might put up earnest money on a house that is next best rather than most preferred, because too many other buyers are bidding on the better alternative. If that other house happens to become available then the buyer might go for that and surrender the earnest money. Similarly, in a buyer's market (excess supply) the buyer might plan to buy the new house assuming the old house will be sold. If that proves difficult, the buyer might chicken out and surrender the earnest money rather than risk having to finance two homes over an extended period of time. (And it should be noted that the buyer faces a like risk, particularly in a seller's market when another buyer may step in and outbid the current best offer. Still another factor is just how flexible and easy to deal with a buyer is. Normally, it is easier to do business with someone who is flexible.
We conclude that there are legitimate reasons for why a buyer may want to buy a particular house and for why a seller may want to sell to a particular buyer. In this case they will almost certainly negotiate about price (and other things too such as the close date and whether repairs will be made on the house prior to closing). The bargaining can itself be a source of price variation. We can't predict precisely how it will turn out. It won't always be like we assumed in the "Trade" worksheet of the S&D Updated workbook, where the price was right in the middle between the buyer's value and the seller's cost. But we do know that it will be determined somehow so they both make out from the deal.
What is your personal experience with bargaining? Have you ever been in a negotiation where you swapped something for something else or bought or sold something at a garage sale or bazaar? If so, can you recall whether it turned out just as you thought it would before the process started?