Chapter 17. Matching, Allocation, and Exchange of Discrete Resources

We present a survey of the emerging literature on the design of matching markets. We survey the articles on discrete resource allocation problems, their solutions, and their applications in three related domains. The first domain gives the theoretical background regarding the basic models, namely house allocation and exchange problems. First, we investigate the allocation and exchange problems separately, and then we combine them to present a real-life application: on-campus housing at universities. As the second application domain, we extend the basic allocation and exchange models to the kidney exchange problem and present new theory and applications regarding this problem. We present proposed and adopted mechanisms that take very specific institutional details into account. Then, we present the school admissions problem in three subcategories: the college admissions model where both schools and students are strategic agents, the school placement model where only students are strategic agents and they induce an endogenous priority structure of schools over students, and finally the school choice model for the US public school districts where the students are the only strategic agents and the school priorities over the students are exogenous. In the final chapter, we investigate the basic models of the axiomatic mechanism design literature that present mechanisms that are generalizations of the mechanisms designed for the specific market design problems discussed before.