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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. As a motivating example, assume that the government plans to build a primary school along a street; an agent with single-peaked preferences would prefer having the school built exactly next to her house. However, while that would make it very easy for her children to go to school, it would also introduce several problems, such as noise or parking congestion in the morning. A 5-min walking distance would be sufficiently far for such problems to no longer be much of a factor and at the same time sufficiently close for the school to be easily accessible by the children on foot. There are two positions (symmetrically) in each direction and those would be the agent’s two peaks of her double-peaked preference. Motivated by natural scenarios like the one described above, 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, which makes the problem 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 strategyproof mechanisms, there is no deterministic mechanism that outperforms our truthful-in-expectation mechanism. In order to obtain this result, we first characterize mechanisms for two agents that satisfy two simple properties; we use the same characterization to prove that no mechanism in this class can be group-strategyproof.
Facility location, Strategyproofness , Maximum cost, Social cost , Approximate mechanism design without money, Double-peaked preferences
1387-2532
1209–1235
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 (2017) Facility location with double-peaked preferences. Autonomous Agents and Multi-Agent Systems, 31 (6), 1209–1235. (doi:10.1007/s10458-017-9361-0).

Record type: Article

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. As a motivating example, assume that the government plans to build a primary school along a street; an agent with single-peaked preferences would prefer having the school built exactly next to her house. However, while that would make it very easy for her children to go to school, it would also introduce several problems, such as noise or parking congestion in the morning. A 5-min walking distance would be sufficiently far for such problems to no longer be much of a factor and at the same time sufficiently close for the school to be easily accessible by the children on foot. There are two positions (symmetrically) in each direction and those would be the agent’s two peaks of her double-peaked preference. Motivated by natural scenarios like the one described above, 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, which makes the problem 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 strategyproof mechanisms, there is no deterministic mechanism that outperforms our truthful-in-expectation mechanism. In order to obtain this result, we first characterize mechanisms for two agents that satisfy two simple properties; we use the same characterization to prove that no mechanism in this class can be group-strategyproof.

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More information

Accepted/In Press date: 1 March 2017
e-pub ahead of print date: 20 March 2017
Published date: November 2017
Keywords: Facility location, Strategyproofness , Maximum cost, Social cost , Approximate mechanism design without money, Double-peaked preferences
Organisations: Agents, Interactions & Complexity

Identifiers

Local EPrints ID: 410712
URI: https://eprints.soton.ac.uk/id/eprint/410712
ISSN: 1387-2532
PURE UUID: caebc625-5c7a-406b-9b85-76fbbba0daa3
ORCID for Jie Zhang: ORCID iD orcid.org/0000-0003-1380-9952

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Date deposited: 09 Jun 2017 09:25
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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