Facility Location Games with Fractional Preferences

Research output: Chapters, Conference Papers, Creative and Literary WorksRGC 32 - Refereed conference paper (with host publication)peer-review

42 Scopus Citations
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Detail(s)

Original languageEnglish
Title of host publication32nd AAAI Conference on Artificial Intelligence (AAAI-18)
PublisherAAAI Press
Pages1039-1046
ISBN (Print)9781577358008
Publication statusPublished - Feb 2018

Publication series

NameAAAI Conference on Artificial Intelligence
PublisherAAAI Press
ISSN (Electronic)2374-3468

Conference

Title32nd AAAI Conference on Artificial Intelligence (AAAI-18)
LocationHilton New Orleans Riverside
PlaceUnited States
CityNew Orleans
Period2 - 7 February 2018

Abstract

In this paper, we propose a fractional preference model for the facility location game with two facilities that serve the similar purpose on a line where each agent has his location information as well as fractional preference to indicate how well they prefer the facilities. The preference for each facility is in the range of [0, L] such that the sum of the preference for all facilities is equal to 1. The utility is measured by subtracting the sum of the cost of both facilities from the total length L where the cost of facilities is defined as the multiplication of the fractional preference and the distance between the agent and the facilities. We first show that the lower bound for the objective of minimizing total cost is at least Ω(n). Hence, we use the utility function to analyze the agents’ satification. Our objective is to place two facilities on [0, L] to maximize the social utility or the minimum utility. For each objective function, we propose deterministic strategy-proof mechanisms. For the objective of maximizing the social utility, we present an optimal deterministic strategy-proof mechanism in the case where agents can only misreport their locations. In the case where agents can only misreport their preferences, we present a 2-approximation deterministic strategy-proof mechanism. Finally, we present a 4-approximation deterministic strategy-proof mechanism and a randomized strategy-proof mechanism with an approximation ratio of 2 where agents can misreport both the preference and location information. Moreover, we also give a lower-bound of 1.06. For the objective of maximizing the minimum utility, we give a lower-bound of 1.5 and present a 2-approximation deterministic strategy-proof mechanism where agents can misreport both the preference and location.

Citation Format(s)

Facility Location Games with Fractional Preferences. / Fong, Ken C.K. ; Li, Minming; Lu, Pinyan et al.
32nd AAAI Conference on Artificial Intelligence (AAAI-18). AAAI Press, 2018. p. 1039-1046 (AAAI Conference on Artificial Intelligence).

Research output: Chapters, Conference Papers, Creative and Literary WorksRGC 32 - Refereed conference paper (with host publication)peer-review