Abstract
We study the mechanism design for discrete facility location games with different preferences, where the facilities can only be built at a finite set of candidate locations, and a mechanism maps the agent locations to candidate locations for building facilities. We consider both the obnoxious preferences, where the agents want to stay as far away as possible from the facilities, and the dual preferences, where each agent may either like or dislike a facility. When the preferences are obnoxious, for two heterogeneous facilities, we present a group strategy-proof mechanism which has an approximation ratio of 2 for both social utility objective and minimum utility objective. Both objectives are proven to have a lower bound of \(\frac{3}{2}\). For two homogeneous facilities, we prove there is no deterministic strategy-proof mechanism with bounded approximation ratio. When the preferences are dual, we consider the single facility location games under the social utility objective, and propose a group strategy-proof mechanism with approximation ratio of 4.
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References
Anastasiadis Eleftherios, Deligkas Argyrios (2018) Heterogeneous facility location games. In Proceedings of the 17th International Conference on Autonomous Agents and MultiAgent Systems (AAMAS), pp 623–631
Chan Hau, Filos-Ratsikas Aris, Li Bo, Li Minming, Wang Chenhao (2021) Mechanism design for facility location problems: a survey. In Proceedings of the 30th International Joint Conference on Artificial Intelligence (IJCAI), pp 4356–4365
Chen Xujin, Xiaodong Hu, Tang Zhongzheng, Wang Chenhao (2021) Tight efficiency lower bounds for strategy-proof mechanisms in two-opposite-facility location game. Inf Process Lett 168:106098
Cheng Yukun, Wei Yu, Zhang Guochuan (2013) Strategy-proof approximation mechanisms for an obnoxious facility game on networks. Theoret Comput Sci 497:154–163
Dokow Elad, Feldman Michal, Meir Reshef, Nehama Ilan (2012) Mechanism design on discrete lines and cycles. In Proceedings of the 13th Acm Conference on Electronic Commerce (EC), pp 423–440
Feldman Michal, Fiat Amos, Golomb Iddan (2016) On voting and facility location. In Proceedings of the 17th ACM Conference on Economics and Computation (EC), pp 269–286
Filimonov Alina, Meir Reshef (2021) Strategyproof facility location mechanisms on discrete trees. In Proceedings of the 20th International Conference on Autonomous Agents and Multiagent Systems (AAMAS), pp 510–518
Gai Ling, Liang Mengpei, Wang Chenhao (2022) Obnoxious facility location games with candidate locations. In Proceedings of the 16th International Conference on Algorithmic Aspects in Information and Management (AAIM), pp 96–105
Kanellopoulos Panagiotis, Voudouris Alexandros, Zhang Rongsen (2022) On discrete truthful heterogeneous two-facility location. In Proceedings of the 31st International Joint Conference on Artificial Intelligence (IJCAI), pp 342–348
Panagiotis Kanellopoulos, Voudouris Alexandros A, Rongsen Zhang (2023) On discrete truthful heterogeneous two-facility location. SIAM J Discret Math 37(2):779–799
Nehama Ilan, Todo Taiki, Yokoo Makoto (2022) Manipulation-resistant false-name-proof facility location mechanisms for complex graphs. Auton Agent Multi-Agent Syst 36(1):12
Procaccia Ariel D, Tennenholtz Moshe (2009) Approximate mechanism design without money. In Proceedings of the 10th ACM Conference on Electronic Commerce (EC), pp 177–186
Serafino Paolo, Ventre Carmine (2016) Heterogeneous facility location without money. Theoret Comput Sci 636:27–46
Tang Zhongzheng, Wang Chenhao, Zhang Mengqi, Zhao Yingchao (2020) Mechanism design for facility location games with candidate locations. In Proceedings of the 14th International Conference on Combinatorial Optimization and Applications (COCOA), pp 440–452
Tang Zhongzheng, Wang Chenhao, Zhang Mengqi, Zhao Yingchao (2022) Strategyproof facility location with limited locations. Journal of the Operations Research Society of China, pp 1–15
Thang Nguyen Kim (2010) On (group) strategy-proof mechanisms without payment for facility location games. In Proceedings of the 6th International Workshop on Internet and Network Economics (WINE), pp 531–538
Walsh Toby (2021) Strategy proof mechanisms for facility location at limited locations. In Proceedings of the 18th Pacific Rim International Conference on Artificial Intelligence (PRICAI), pp 113–124
Xinping Xu, Li Bo, Li Minming, Duan Lingjie (2021) Two-facility location games with minimum distance requirement. J Artif Intell Res 70:719–756
Zou Shaokun, Li Minming (2015) Facility location games with dual preference. In Proceedings of the 14th International Conference on Autonomous Agents and MultiAgent Systems (AAMAS), pp 615–623
Funding
This work was supported in part by the Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, UIC, project code 2022B1212010006, by Guangdong Higher Education Upgrading Plan (2021–2025) of “Rushing to the Top, Making Up Shortcomings and Strengthening Special Features” with UIC research grant R0400001-22, and by Artificial Intelligence and Data Science Research Hub, UIC, No. 2020KSYS007 and No. UICR0400025-21. Ling Gai is supported by National Natural Science Foundation of China under Grant No. 11201333. Chenhao Wang is supported by NSFC under Grant No. 12201049, and is also supported by UIC grants of UICR0400014-22, UICR0200008-23 and UICR0700036-22.
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Gai, L., Liang, M. & Wang, C. Discrete facility location games with different preferences. J Comb Optim 46, 17 (2023). https://doi.org/10.1007/s10878-023-01082-x
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DOI: https://doi.org/10.1007/s10878-023-01082-x