Chapters 7, 8, and 9 present three models of one-to-one matching in which money plays a prominent role. Unlike the model explored in Section 6.2, money will be modeled as a continuous rather than as a discrete variable, and this will let us employ a different set of mathematical tools. An even more important difference between the models of these chapters and those we have dealt with until now is that in these models, we are going to assume that the preferences individuals have for different matchings are basically monetary in nature.

Chapter 7 presents a model of exchange between one seller, with a single object to sell, and many buyers. This model will be simple enough so that the analysis can be conducted without much technical apparatus. We will explore it in enough detail to see that with one or two significant exceptions, the phenomena uncovered in our presentation of the marriage problem will also arise in these models with money. We will also relate this discussion to our discussion in Section 1.2 of strategic behavior in auctions, and particularly to the options available to coalitions of bidders.