Improving Ef ® ciency of On - Campus Housing : An Experimental Study

This paper investigates a class of matching problems—the assignment of indivisible items to agents where some agents have prior claims to some of the items. As a running example, we will refer to the indivisible items as houses. House allocation problems are not only of theoretical interest, but also of practical importance. A house allocation mechanism assigns a set of houses (or ofŽ ces, tasks, etc.) to prospective tenants, allotting at most one house to each tenant. Rents are exogenously given and there is no medium of exchange, such as money. In general some houses will have existing tenants, some houses will be empty, and some applicants for housing will be new (e.g., freshmen). The canonical examples are assignment of college students to dormitory rooms and public housing units. Other examples are assignment of ofŽ ces and tasks to individuals. Many universities in the United States employ some variant of a mechanism called the random serial dictatorshipwith squatting rights (RSD) to allocate dormitory rooms. Each existing tenant can either keep her house or enter the applicant pool. Each applicant is randomly given a (possibly seniority-weighted or GPAweighted) priority and each is assigned, in priority order, her top choice among the houses that remain. This mechanism is strategy-proof (i.e., dominant strategy incentive compatible): truthful preference revelation is a dominant strategy for each applicant (Lin Zhou, 1990). On the negative side, a tenant who enters the lottery may end up with a house that is worse than her current house. As a result not every existing tenant joins the applicant pool, potential gains from trade are lost, and the mechanism yields Pareto-inefŽ cient outcomes (Atila Abdulkadirog  lu and Sönmez, 1999). While we are not aware of any systematic Ž eld studies of this mechanism, there is some evidence for this inefŽ ciency. For example, at the University of Michigan, where RSD is used to assign undergraduate students to residence halls, there is a restricted after-market for leases. Motivated by these observations, Abdulkadirog lu and Sönmez (1999) propose a simple mechanism, the top trading cycles (TTC) mechanism, as a superior alternative. In this mechanism, applicants are again prioritized and are given their top choice in priority order. This process continues until someone requests an existing tenant’s house. In this case, the existing tenant is moved to the top of the priority queue, directly in front of the requester. If a cycle of requests is formed (e.g., I want John’s house, John wants your house, and you want my house), all members of the cycle are given what they want, and their new houses are removed from the system. This mechanism is theoretically superior to the former: it is strategy-proof, individually rational, and Pareto efŽ cient. * Chen: School of Information, University of Michigan, 550 East University Avenue, Ann Arbor, MI 48109 (e-mail: [email protected]); Sönmez: Department of Economics, Koç University, Sar‡yer, 80910, Istanbul, Turkey (e-mail: [email protected]). We thank Rachel Croson, Julie Cullen, Catherine Eckel, Elisabeth Hoffman, Lutz Kilian, David Lucking-Reiley, David Pennock, Laura Razzolini, Stephane Robin, Larry Samuelson, Sara Solnick, Lise Vesterlund, two anonymous referees, anonymous referees of the National Science Foundation, and seminar participants at the University of Aarhus, University of Copenhagen, Harvard University, Hong KongUniversity of Science and Technology,LundUniversity, University of Michigan, Rice University, University of St. Gallen, University of Zürich, the 1999 and 2000 ESA meetings, and SED 2000 meetings for helpful comments and discussions. Yuri Khoroshilov, Emre Sucu, Chun-Chih Chen, Sharon Lam, and Asad Qayyum provided excellent research assistance. Financial support from the National Science Foundation through Grant No. SBR-9805586 to Chen and SES-9904214 to Sönmez are gratefully acknowledged. Any remaining errors are our own. 1 The Michigan Reapplication Lease Renewal Program (University Housing, 1999, p. 4) states that a returning student can only reassign a lease to a newly entering student. Returning students are not allowed to buy or sell leases from each other. In 1999 the application and assignment process was in February and March, while the after-market did not begin until August 2.