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Size versus truthfulness in the house allocation problem

Size versus truthfulness in the house allocation problem
Size versus truthfulness in the house allocation problem
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.
453-470
ACM
Krysta, Piotr
7da6810f-0299-486a-86c3-6e4c4127ef30
Manlove, David
a4321a32-3611-4a9f-9dfe-c595dc7a5a38
Rastegari, Baharak
6ba9e93c-53ba-4090-8f77-c1cb1568d7d1
Zhang, Jinshan
dceaf1fe-451c-4cdd-87d8-1ed661bf468e
Krysta, Piotr
7da6810f-0299-486a-86c3-6e4c4127ef30
Manlove, David
a4321a32-3611-4a9f-9dfe-c595dc7a5a38
Rastegari, Baharak
6ba9e93c-53ba-4090-8f77-c1cb1568d7d1
Zhang, Jinshan
dceaf1fe-451c-4cdd-87d8-1ed661bf468e

Krysta, Piotr, Manlove, David, Rastegari, Baharak and Zhang, Jinshan (2014) Size versus truthfulness in the house allocation problem. In EC '14 Proceedings of the fifteenth ACM conference on Economics and computation. ACM. pp. 453-470 . (doi:10.1145/2600057.2602868).

Record type: Conference or Workshop Item (Paper)

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.

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More information

Published date: 2014
Venue - Dates: the fifteenth ACM conference, Palo Alto, California, USA, 2014-06-08 - 2014-06-12

Identifiers

Local EPrints ID: 426400
URI: http://eprints.soton.ac.uk/id/eprint/426400
PURE UUID: 68a052d7-6bde-4abe-a397-ffd94297df2d
ORCID for Baharak Rastegari: ORCID iD orcid.org/0000-0002-0985-573X

Catalogue record

Date deposited: 27 Nov 2018 17:30
Last modified: 10 Nov 2021 03:56

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Contributors

Author: Piotr Krysta
Author: David Manlove
Author: Baharak Rastegari ORCID iD
Author: Jinshan Zhang

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