House Allocation When Construction Schedule is Unpredictable

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, it often happens that more objects, sometimes fewer objects are available than initially planned and allocated. How should such changes be handled? The first perspective that we may take is to declare the initial decision irrelevant. We simply cancel it and allocate all available objects. Alternatively, we can use the initial decision as starting point in allocating the new objects. 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. This is the first paper that applies the general robustness principle to the objects assignment problem. 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 sequential priority rules: given a priority order over people, they arrive one at a time, and each picks his/her most preferred object among the remaining ones. Our results provide additional theoretical support for the sequential priority rules