Mathematical Social Sciences 81 (2016) 29–37 Contents lists available at ScienceDirect Mathematical Social Sciences journal homepage: www.elsevier.com/locate/econbase House allocation when availability of houses may change unexpectedly ✩ Azar Abizada a,∗ , Siwei Chen b a School of Business, ADA University, 11 Ahmadbay Aghaoglu St., Baku AZ1008, Azerbaijan b Lingnan College, Sun Yat-Sen University, Guangzhou, 510275, China article info Article history: Received 11 February 2014 Received in revised form 20 February 2016 Accepted 1 March 2016 Available online 19 March 2016 abstract We study the problem of allocating a set of objects, e.g. houses, tasks, offices to a group of people having preferences over these objects. For various reasons, there may be more or fewer objects than initially planned and allocated. How should such unexpected changes be handled? One way is to declare the initial decision irrelevant and reallocate all available objects. Alternatively, one can use the initial decision as starting point in allocating the new objects. Since both perspectives seem equally reasonable, a natural robustness principle on the rule is that it should produce the same outcome no matter which one is taken. We define two robustness properties based on this idea, pertaining to more objects and fewer objects, respectively. We characterize the family of rules that satisfy mild efficiency, fairness and incentives requirements, together with either one of our robustness properties. They are the family of serial dictatorship rules. © 2016 Elsevier B.V. All rights reserved. 1. Introduction Many universities offer on-campus housing for their faculty members. Each year, a university has to allocate the available houses among the new faculty members. Each faculty member can receive at most one house. The faculty members have the outside option of living off campus. The university provides the new faculty members with the complete list of houses (vacant or not). Each faculty member then submits strict preferences over the houses and the outside option. We look for rules allocating houses to faculty members. Some other applications of our model are assigning vacant offices among new employees, assigning on campus apartments among new graduate students, and so on. A house is an indivisible good, or ‘‘object’’. The problem of allocating objects among people is first studied by Hylland and Zeckhauser (1979). In the basic model, the set of objects is fixed, and each person receives at most one object. Various properties of efficiency, fairness, and robustness under strategic behavior ✩ We would like to thank William Thomson for his guidance, and invaluable comments. We also would like to thank two anonymous referees and the participants of GAMES 2012 and SED 2013 for their feedbacks. ∗ Corresponding author. E-mail addresses: aabizada@ada.edu.az (A. Abizada), chensw6@mail.sysu.edu.cn (S. Chen). have been analyzed in this context (Hylland and Zeckhauser, 1979; Svensson, 1999; Ergin, 2000; Ehlers and Klaus, 2004; Bu, 2012). We consider situations where the set of objects is not fixed. Throughout the paper, we will use the example of on-campus housing for faculty members. Although in real life, the assignment procedure may not be exactly the same as described here, we choose this (partially artificial) example for two reasons: (i) it does capture important features of real-life problems, (ii) it helps us explain the key notions clearly and intuitively. Suppose that an assignment of available houses among incoming faculty members has been made. Closer to the arrival of the new faculty members, it may happen that some houses become unavailable: some current faculty members who were supposed to terminate their leases choose to extend their stay. Thus, their current houses become unavailable for this year. It is also possible that some additional houses become available: some current faculty members decide to terminate their leases earlier (either they move off campus or for some other reason). Thus, their houses become vacant. When one of these unexpected changes happens, how should university handle it? In general, when the circumstances in which a group of people find themselves change, there might be several perspectives that can be taken and the document binding the people as a group may not always specify which one should be chosen. Yet, outcomes may differ depending on which perspective is taken. When outcomes differ, no matter what action is chosen, someone maybe unhappy http://dx.doi.org/10.1016/j.mathsocsci.2016.03.002 0165-4896/© 2016 Elsevier B.V. All rights reserved.