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Two-sided matching with partial information

Two-sided matching with partial information
Two-sided matching with partial information
The traditional model of two-sided matching assumes that all agents fully know their own preferences. As markets grow large, however, it becomes impractical for agents to precisely assess their rankings over all agents on the other side of the market. We propose a novel model of two-sided matching in which agents are endowed with known partially ordered preferences and unknown true preferences drawn from known distributions consistent with the partial order. The true preferences are learned through interviews, revealing the pairwise rankings among all interviewed agents, performed according to a centralized interview policy, i.e., an algorithm that adaptively schedules interviews. Our goal is for the policy to guarantee both stability and optimality for a given side of the market, with respect to the underlying true preferences of the agents. As interviews are costly, we seek a policy that minimizes the number of interviews. We introduce three minimization objectives: (very weak) dominance, which minimizes the number of interviews for any underlying true preference profile; Pareto optimality, which guarantees that no other policy dominates the given policy; and optimality in expectation with respect to the preference distribution. We formulate our problem as a Markov decision process, implying an algorithm for computing an optimal-in-expectation policy in time polynomial in the number of possible preference orderings (and thus exponential in the size of the input). We then derive structural properties of dominant policies which we call optimality certificates. We show that computing a minimum optimality certificate is NP-hard, suggesting that optimal-in-expectation and/or Pareto optimal policies could be NP-hard to compute. Finally, we restrict attention to a setting in which agents on one side of the market have the same partially ordered preferences (but potentially distinct underlying true preferences), and in which agents must interview before matching. In this restricted setting, we show how to leverage the idea of minimum optimality certificates to design a computationally efficient interview-minimizing policy. This policy works without knowledge of the distributions and is dominant (and so is also Pareto optimal and optimal-in-expectation).
733-750
ACM
Rastegari, Baharak
6ba9e93c-53ba-4090-8f77-c1cb1568d7d1
Condon, Anne
a1c1e645-b4b0-4449-a18e-6e43a440cce8
Immorlica, Nicole
df5133d6-b6e0-4486-8798-b25d962fe389
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
Leyton-brown, Kevin
bbf18b1f-b857-48b6-b33c-5b26a6ed6b13

Rastegari, Baharak, Condon, Anne, Immorlica, Nicole and Leyton-brown, Kevin (2013) Two-sided matching with partial information. In EC '13 Proceedings of the Fourteenth ACM Conference on Electronic Commerce. ACM. pp. 733-750 . (doi:10.1145/2492002.2482607).

Record type: Conference or Workshop Item (Paper)

Abstract

The traditional model of two-sided matching assumes that all agents fully know their own preferences. As markets grow large, however, it becomes impractical for agents to precisely assess their rankings over all agents on the other side of the market. We propose a novel model of two-sided matching in which agents are endowed with known partially ordered preferences and unknown true preferences drawn from known distributions consistent with the partial order. The true preferences are learned through interviews, revealing the pairwise rankings among all interviewed agents, performed according to a centralized interview policy, i.e., an algorithm that adaptively schedules interviews. Our goal is for the policy to guarantee both stability and optimality for a given side of the market, with respect to the underlying true preferences of the agents. As interviews are costly, we seek a policy that minimizes the number of interviews. We introduce three minimization objectives: (very weak) dominance, which minimizes the number of interviews for any underlying true preference profile; Pareto optimality, which guarantees that no other policy dominates the given policy; and optimality in expectation with respect to the preference distribution. We formulate our problem as a Markov decision process, implying an algorithm for computing an optimal-in-expectation policy in time polynomial in the number of possible preference orderings (and thus exponential in the size of the input). We then derive structural properties of dominant policies which we call optimality certificates. We show that computing a minimum optimality certificate is NP-hard, suggesting that optimal-in-expectation and/or Pareto optimal policies could be NP-hard to compute. Finally, we restrict attention to a setting in which agents on one side of the market have the same partially ordered preferences (but potentially distinct underlying true preferences), and in which agents must interview before matching. In this restricted setting, we show how to leverage the idea of minimum optimality certificates to design a computationally efficient interview-minimizing policy. This policy works without knowledge of the distributions and is dominant (and so is also Pareto optimal and optimal-in-expectation).

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More information

Published date: 2013
Venue - Dates: the fourteenth ACM conference, Philadelphia, Pennsylvania, USA, 2013-06-16 - 2013-06-20

Identifiers

Local EPrints ID: 426399
URI: http://eprints.soton.ac.uk/id/eprint/426399
PURE UUID: b30b60ec-4dae-4944-9853-c2aa4bd91354
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: Baharak Rastegari ORCID iD
Author: Anne Condon
Author: Nicole Immorlica
Author: Kevin Leyton-brown

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