In the obnoxious facility game, we design mechanisms that output a location of an undesirable facility based on the locations of players reported by themselves. The benefit of a player is defined to be the distance between her location and the facility. A player may try to manipulate the output of the mechanism by strategically misreporting her location. We wish to design a λ-group strategy-proof mechanism i.e., for every group of players, at least one player in the group cannot gain strictly more than λ times her primary benefit by having the entire group change their reports simultaneously. In this paper, we design a k-candidate λ-group strategy-proof mechanism for the obnoxious facility game in the metric defined by k half lines with a common endpoint such that each candidate is a point in each of the half-lines at the same distance to the common endpoint as other candidates. Then, we show that the benefit ratio of the mechanism is at most 1+2/(k-1)λ. Finally, we prove that the bound is nearly tight.
Yuhei FUKUI
Kyoto University
Aleksandar SHURBEVSKI
Kyoto University
Hiroshi NAGAMOCHI
Kyoto University
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Yuhei FUKUI, Aleksandar SHURBEVSKI, Hiroshi NAGAMOCHI, "λ-Group Strategy-Proof Mechanisms for the Obnoxious Facility Game in Star Networks" in IEICE TRANSACTIONS on Fundamentals,
vol. E102-A, no. 9, pp. 1179-1186, September 2019, doi: 10.1587/transfun.E102.A.1179.
Abstract: In the obnoxious facility game, we design mechanisms that output a location of an undesirable facility based on the locations of players reported by themselves. The benefit of a player is defined to be the distance between her location and the facility. A player may try to manipulate the output of the mechanism by strategically misreporting her location. We wish to design a λ-group strategy-proof mechanism i.e., for every group of players, at least one player in the group cannot gain strictly more than λ times her primary benefit by having the entire group change their reports simultaneously. In this paper, we design a k-candidate λ-group strategy-proof mechanism for the obnoxious facility game in the metric defined by k half lines with a common endpoint such that each candidate is a point in each of the half-lines at the same distance to the common endpoint as other candidates. Then, we show that the benefit ratio of the mechanism is at most 1+2/(k-1)λ. Finally, we prove that the bound is nearly tight.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E102.A.1179/_p
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@ARTICLE{e102-a_9_1179,
author={Yuhei FUKUI, Aleksandar SHURBEVSKI, Hiroshi NAGAMOCHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={λ-Group Strategy-Proof Mechanisms for the Obnoxious Facility Game in Star Networks},
year={2019},
volume={E102-A},
number={9},
pages={1179-1186},
abstract={In the obnoxious facility game, we design mechanisms that output a location of an undesirable facility based on the locations of players reported by themselves. The benefit of a player is defined to be the distance between her location and the facility. A player may try to manipulate the output of the mechanism by strategically misreporting her location. We wish to design a λ-group strategy-proof mechanism i.e., for every group of players, at least one player in the group cannot gain strictly more than λ times her primary benefit by having the entire group change their reports simultaneously. In this paper, we design a k-candidate λ-group strategy-proof mechanism for the obnoxious facility game in the metric defined by k half lines with a common endpoint such that each candidate is a point in each of the half-lines at the same distance to the common endpoint as other candidates. Then, we show that the benefit ratio of the mechanism is at most 1+2/(k-1)λ. Finally, we prove that the bound is nearly tight.},
keywords={},
doi={10.1587/transfun.E102.A.1179},
ISSN={1745-1337},
month={September},}
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TY - JOUR
TI - λ-Group Strategy-Proof Mechanisms for the Obnoxious Facility Game in Star Networks
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1179
EP - 1186
AU - Yuhei FUKUI
AU - Aleksandar SHURBEVSKI
AU - Hiroshi NAGAMOCHI
PY - 2019
DO - 10.1587/transfun.E102.A.1179
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E102-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2019
AB - In the obnoxious facility game, we design mechanisms that output a location of an undesirable facility based on the locations of players reported by themselves. The benefit of a player is defined to be the distance between her location and the facility. A player may try to manipulate the output of the mechanism by strategically misreporting her location. We wish to design a λ-group strategy-proof mechanism i.e., for every group of players, at least one player in the group cannot gain strictly more than λ times her primary benefit by having the entire group change their reports simultaneously. In this paper, we design a k-candidate λ-group strategy-proof mechanism for the obnoxious facility game in the metric defined by k half lines with a common endpoint such that each candidate is a point in each of the half-lines at the same distance to the common endpoint as other candidates. Then, we show that the benefit ratio of the mechanism is at most 1+2/(k-1)λ. Finally, we prove that the bound is nearly tight.
ER -