### 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 mini-1 mizing total cost is at least Ω(n3). 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 strategyproof 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 strategyproof mechanism where agents can misreport both the preference and location.

Original language | English |
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Title of host publication | 32nd AAAI Conference on Artificial Intelligence, AAAI 2018 |

Publisher | AAAI Press |

Pages | 1039-1046 |

Number of pages | 8 |

ISBN (Electronic) | 9781577358008 |

Publication status | Published - Jan 1 2018 |

Event | 32nd AAAI Conference on Artificial Intelligence, AAAI 2018 - New Orleans, United States Duration: Feb 2 2018 → Feb 7 2018 |

### Publication series

Name | 32nd AAAI Conference on Artificial Intelligence, AAAI 2018 |
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### Conference

Conference | 32nd AAAI Conference on Artificial Intelligence, AAAI 2018 |
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Country | United States |

City | New Orleans |

Period | 2/2/18 → 2/7/18 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Artificial Intelligence

### Cite this

*32nd AAAI Conference on Artificial Intelligence, AAAI 2018*(pp. 1039-1046). (32nd AAAI Conference on Artificial Intelligence, AAAI 2018). AAAI Press.

**Facility location games with fractional preferences.** / Fong, Ken C.K.; Li, Minming; Lu, Pinyan; Todo, Taiki; Yokoo, Makoto.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*32nd AAAI Conference on Artificial Intelligence, AAAI 2018.*32nd AAAI Conference on Artificial Intelligence, AAAI 2018, AAAI Press, pp. 1039-1046, 32nd AAAI Conference on Artificial Intelligence, AAAI 2018, New Orleans, United States, 2/2/18.

}

TY - GEN

T1 - Facility location games with fractional preferences

AU - Fong, Ken C.K.

AU - Li, Minming

AU - Lu, Pinyan

AU - Todo, Taiki

AU - Yokoo, Makoto

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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 mini-1 mizing total cost is at least Ω(n3). 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 strategyproof 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 strategyproof mechanism where agents can misreport both the preference and location.

AB - 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 mini-1 mizing total cost is at least Ω(n3). 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 strategyproof 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 strategyproof mechanism where agents can misreport both the preference and location.

UR - http://www.scopus.com/inward/record.url?scp=85055341073&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85055341073&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85055341073

T3 - 32nd AAAI Conference on Artificial Intelligence, AAAI 2018

SP - 1039

EP - 1046

BT - 32nd AAAI Conference on Artificial Intelligence, AAAI 2018

PB - AAAI Press

ER -