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Reasoning about optimal stable matchings under partial information

Reasoning about optimal stable matchings under partial information
Reasoning about optimal stable matchings under partial information
We study two-sided matching markets in which participants are initially endowed with partial preference orderings, lacking precise information about their true, strictly ordered list of preferences. We wish to reason about matchings that are stable with respect to agents' true preferences, and which are furthermore optimal for one given side of the market. We present three main results. First, one can decide in polynomial time whether there exists a matching that is stable and optimal under all strict preference orders that refine the given partial orders, and can construct this matching in polynomial time if it does exist. We show, however, that deciding whether a given pair of agents are matched in all or no such optimal stable matchings is co-NP-complete, even under quite severe restrictions on preferences. Finally, we describe a polynomial-time algorithm that decides, given a matching that is stable under the partial preference orderings, whether that matching is stable and optimal for one side of the market under some refinement of the partial orders.
431-448
ACM
Rastegari, Baharak
6ba9e93c-53ba-4090-8f77-c1cb1568d7d1
Condon, Anne
a1c1e645-b4b0-4449-a18e-6e43a440cce8
Immorlica, Nicole
df5133d6-b6e0-4486-8798-b25d962fe389
Irving, Robert
8a14d692-23cf-4403-bcb8-0cd87c49d93e
Leyton-brown, Kevin
bbf18b1f-b857-48b6-b33c-5b26a6ed6b13
Rastegari, Baharak
6ba9e93c-53ba-4090-8f77-c1cb1568d7d1
Condon, Anne
a1c1e645-b4b0-4449-a18e-6e43a440cce8
Immorlica, Nicole
df5133d6-b6e0-4486-8798-b25d962fe389
Irving, Robert
8a14d692-23cf-4403-bcb8-0cd87c49d93e
Leyton-brown, Kevin
bbf18b1f-b857-48b6-b33c-5b26a6ed6b13

Rastegari, Baharak, Condon, Anne, Immorlica, Nicole, Irving, Robert and Leyton-brown, Kevin (2014) Reasoning about optimal stable matchings under partial information. In Proceedings of the Fifteenth ACM Conference on Economics and Computation. ACM. pp. 431-448 . (doi:10.1145/2600057.2602884).

Record type: Conference or Workshop Item (Paper)

Abstract

We study two-sided matching markets in which participants are initially endowed with partial preference orderings, lacking precise information about their true, strictly ordered list of preferences. We wish to reason about matchings that are stable with respect to agents' true preferences, and which are furthermore optimal for one given side of the market. We present three main results. First, one can decide in polynomial time whether there exists a matching that is stable and optimal under all strict preference orders that refine the given partial orders, and can construct this matching in polynomial time if it does exist. We show, however, that deciding whether a given pair of agents are matched in all or no such optimal stable matchings is co-NP-complete, even under quite severe restrictions on preferences. Finally, we describe a polynomial-time algorithm that decides, given a matching that is stable under the partial preference orderings, whether that matching is stable and optimal for one side of the market under some refinement of the partial orders.

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More information

Published date: 1 June 2014
Venue - Dates: EC '14 Fifteenth ACM Conference, Palo Alto, California, USA, 2014-06-08 - 2014-06-12

Identifiers

Local EPrints ID: 426216
URI: http://eprints.soton.ac.uk/id/eprint/426216
PURE UUID: 678349c1-3df6-4ba5-b36d-3e6799a547ce
ORCID for Baharak Rastegari: ORCID iD orcid.org/0000-0002-0985-573X

Catalogue record

Date deposited: 20 Nov 2018 17:30
Last modified: 10 Nov 2021 03:56

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Contributors

Author: Baharak Rastegari ORCID iD
Author: Anne Condon
Author: Nicole Immorlica
Author: Robert Irving
Author: Kevin Leyton-brown

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