NDLI: Size versus truthfulness in the house allocation problem

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Size versus truthfulness in the house allocation problem

Content Provider	ACM Digital Library
Author	Rastegari, Baharak Zhang, Jinshan Manlove, David Krysta, Piotr
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.
Ending Page	470
Page Count	18
Starting Page	453
File Format	PDF
ISBN	9781450325653
DOI	10.1145/2600057.2602868
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2014-06-01
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Assignment problem Pareto optimal matching Randomized mechanisms House allocation problem Truthfulness
Content Type	Text
Resource Type	Article

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