There is a half-open set of prices the buyer will pay: [0..max). There is a half-open set of prices the seller will accept: (min..$\infty$] If these sets do n

There is a half-open set of prices the buyer will pay: [0..max). There is a half-open set of prices the seller will accept: (min..$\infty$] If these sets do not intersect, there's no deal no matter what the agents do. If the sets do intersect, the agents collude to ensure that the sale closes at the HIGHEST price in the intersection. That is why realtors are such a big factor in the housing crisis. They collude to push all of the transactional surplus to the seller, because both agents work for the seller.