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Facility location with double-peaked preferences

Facility location with double-peaked preferences
Facility location with double-peaked preferences
We study the problem of locating a single facility on a real line based on the reports of self-interested agents, when agents have double-peaked preferences, with the peaks being on opposite sides of their locations.We observe that double-peaked preferences capture real-life scenarios and thus complement the well-studied notion of single-peaked preferences. We mainly focus on the case where peaks are equidistant from the agents’ locations and discuss how our results extend to more general settings. We show that most of the results for single-peaked preferences do not directly apply to this setting; this makes the problem essentially more challenging. As our main contribution, we present a simple truthful-in-expectation mechanism that achieves an approximation ratio of 1+b/c for both the social and the maximum cost, where b is the distance of the agent from the peak and c is the minimum cost of an agent. For the latter case, we provide a 3/2 lower bound on the approximation ratio of any truthful-in-expectation mechanism. We also study deterministic mechanisms under some natural conditions, proving lower bounds and approximation guarantees. We prove that among a large class of reasonable mechanisms, there is no deterministic mechanism that outpeforms our truthful-in-expectation mechanism.
893-899
Filos-Ratsikas, Aris
14e554b2-bc6b-4b2c-a84d-8650ad4bed14
Li, Minming
35621c6a-cf18-45b7-b428-f9b2c2625c08
Zhang, Jie
6bad4e75-40e0-4ea3-866d-58c8018b225a
Zhang, Qiang
7e3b7a43-bfc5-4d7a-8f4b-4e930d6ba356
Filos-Ratsikas, Aris
14e554b2-bc6b-4b2c-a84d-8650ad4bed14
Li, Minming
35621c6a-cf18-45b7-b428-f9b2c2625c08
Zhang, Jie
6bad4e75-40e0-4ea3-866d-58c8018b225a
Zhang, Qiang
7e3b7a43-bfc5-4d7a-8f4b-4e930d6ba356

Filos-Ratsikas, Aris, Li, Minming, Zhang, Jie and Zhang, Qiang (2015) Facility location with double-peaked preferences. pp. 893-899.

Record type: Conference or Workshop Item (Other)

Abstract

We study the problem of locating a single facility on a real line based on the reports of self-interested agents, when agents have double-peaked preferences, with the peaks being on opposite sides of their locations.We observe that double-peaked preferences capture real-life scenarios and thus complement the well-studied notion of single-peaked preferences. We mainly focus on the case where peaks are equidistant from the agents’ locations and discuss how our results extend to more general settings. We show that most of the results for single-peaked preferences do not directly apply to this setting; this makes the problem essentially more challenging. As our main contribution, we present a simple truthful-in-expectation mechanism that achieves an approximation ratio of 1+b/c for both the social and the maximum cost, where b is the distance of the agent from the peak and c is the minimum cost of an agent. For the latter case, we provide a 3/2 lower bound on the approximation ratio of any truthful-in-expectation mechanism. We also study deterministic mechanisms under some natural conditions, proving lower bounds and approximation guarantees. We prove that among a large class of reasonable mechanisms, there is no deterministic mechanism that outpeforms our truthful-in-expectation mechanism.

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e-pub ahead of print date: 16 February 2015
Organisations: Agents, Interactions & Complexity

Identifiers

Local EPrints ID: 402580
URI: https://eprints.soton.ac.uk/id/eprint/402580
PURE UUID: 15731324-a3ae-44ac-a98e-15ba917f3e36
ORCID for Jie Zhang: ORCID iD orcid.org/0000-0003-1380-9952

Catalogue record

Date deposited: 29 Nov 2016 09:39
Last modified: 06 Jun 2018 12:14

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Contributors

Author: Aris Filos-Ratsikas
Author: Minming Li
Author: Jie Zhang ORCID iD
Author: Qiang Zhang

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