Single Unit Trade

In the simplest model of pure exchange each trader has or wants at most one unit of a commodity, depending on whether he is a seller or a buyer. It avoids some needless complications to assume an equal number of buyers and sellers, say n. A buyer has a maximal acceptable price and a seller a minimal acceptable price. Typically one assumes these price limits do not depend on the identity of the other party in a trade. However, an instructive departure from perfect simplicity allows these reservation prices to depend on the traders. Thus let the seller’s reservation price differ by buyer and the buyer’s limit price to differ by seller. Hence a_ij is the lowest price seller A_i would accept from buyer B_j and b_ij the highest price buyer j would pay to seller A_i . There are at least three plausible reasons for such dependence. Take the seller. First, the cost to a seller of dealing with a buyer may depend on the buyer’s characteristics. Second, a seller may try to gauge the buyer’s eagerness for the object and adjust the reservation price accordingly. Third, a seller may not wish to offer the object at the same price to all the buyers for a variety of personal reasons, sometimes called “discriminatory.” Therefore, it is not frivolous to assume a seller has different reservation prices for different buyers and conversely.