Size versus truthfulness in the house allocation problem

Krysta, P., Manlove, D. , Rastegari, B. and Zhang, J. (2014) Size versus truthfulness in the house allocation problem. In: Fifteenth ACM Conference on Economics and Computation (EC'14), Palo Alto, CA USA, 8-12 June 2014, pp. 453-470. (doi:10.1145/2600057.2602868)

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Publisher's URL: http://dx.doi.org/10.1145/2600057.2602868

Abstract

We study the House Allocation problem (also known as the Assignment problem), i.e., the problem of allocating a set of objects among a set of agents, where each agent has ordinal preferences (possibly involving ties) over a subset of the objects. We focus on truthful mechanisms without monetary transfers for finding large Pareto optimal matchings. It is straightforward to show that no deterministic truthful mechanism can approximate a maximum cardinality Pareto optimal matching with ratio better than 2. We thus consider randomized mechanisms. We give a natural and explicit extension of the classical Random Serial Dictatorship Mechanism (RSDM) specifically for the House Allocation problem where preference lists can include ties. We thus obtain a universally truthful randomized mechanism for finding a Pareto optimal matching and show that it achieves an approximation ratio of eovere-1. The same bound holds even when agents have priorities (weights) and our goal is to find a maximum weight (as opposed to maximum cardinality) Pareto optimal matching. On the other hand we give a lower bound of 18 over 13 on the approximation ratio of any universally truthful Pareto optimal mechanism in settings with strict preferences. In the case that the mechanism must additionally be non-bossy, an improved lower bound of eovere-1 holds. This lower bound is tight given that RSDM for strict preference lists is non-bossy. We moreover interpret our problem in terms of the classical secretary problem and prove that our mechanism provides the best randomized strategy of the administrator who interviews the applicants.

Item Type:Conference Proceedings
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Rastegari, Dr Baharak and Manlove, Professor David
Authors: Krysta, P., Manlove, D., Rastegari, B., and Zhang, J.
College/School:College of Science and Engineering > School of Chemistry
Copyright Holders:Copyright © 2014 Association for Computing Machinery
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher.
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
607071Efficient Algorithms for Mechanism Design Without Monetary Transfer.David ManloveEngineering & Physical Sciences Research Council (EPSRC)EP/K010042/1COM - COMPUTING SCIENCE