We study assignment problems in a model where agents have strict preferences over objects, allowing preference lists to be incomplete. We investigate the questions whether an agent can obtain or necessarily obtains a given object under serial dictatorship. We prove that both problems are computationally hard even if agents have preference lists of length at most, 3; by contrast, we give linear-time algorithms for the case where preference lists are of length at most, 2. We also study a capacitated version of these problems where objects come in several copies.
CITATION STYLE
Cechlárová, K., Fleiner, T., & Schlotter, I. (2017). Possible and Necessary Allocations Under Serial Dictatorship with Incomplete Preference Lists. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10576 LNAI, pp. 300–314). Springer Verlag. https://doi.org/10.1007/978-3-319-67504-6_21
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