We study a fairness-based model for 2-facility location games on the real line where the social objective is to minimize the maximum envy over all agents. All the agents seek to minimize their personal costs, and the envy between any two of them is the difference in their personal costs. We consider two cases of personal costs, called min-dist cost and sum-dist cost. We are interested in pursuing strategyproof mechanisms for 2-facility location games in both cases. For the min-dist personal cost, we first show that a lower bound of the additive approximation for any deterministic strategyproof mechanism is 1/4, then devise a deterministic group strategyproof mechanism with additive approximation of 1/2 and two randomized strategyproof mechanisms with additive approximation of 1/4. For the sum-dist personal cost, we devise a group strategyproof deterministic mechanism which is also optimal.
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Alon N, Shapira A, Sudakov B (2009) Additive approximation for edge-deletion problems. Ann Math 170(1):371–411
Alon N, Feldman M, Procaccia AD, Tennenholtz M (2010) Strategyproof approximation of the minimax on networks. Math Oper Res 35(3):513–526. https://doi.org/10.1287/moor.1100.0457
Anastasiadis E, Deligkas A (2018) Heterogeneous facility location games. In: Proceedings of the 17th international conference on autonomous agents and multiagent systems, pp 623–631
Cai Q, Filos-Ratsikas A, Tang P (2016) Facility location with minimax envy. In: Proceedings of the 25th international joint conference on artificial intelligence, pp 137–143
Cheng Y, Wu W, Zhang G (2013) Strategyproof approximation mechanisms for an obnoxious facility game on networks. Theor Comput Sci 497:154–163. https://doi.org/10.1016/j.tcs.2011.11.041
Chen X, Hu X, Jia X, Li M, Tang Z, Wang C (2018) Mechanism design for two-opposite-facility location games with penalties on distance. In: Proceedings of the 11th international symposium, pp 256–260. https://doi.org/10.1007/978-3-319-99660-8
Clarke E (1971) Multipart pricing of public goods. Public Choices 11:17–33
Ding Y, Liu W, Chen X, Fang Q, Nong Q (2020) Facility location game with envy ratio. Comput Ind Eng 148:106710. https://doi.org/10.1016/j.cie.2020.106710
Duan L, Li B, Li M, Xu X (2019) Heterogenious two-facility location games with minimum distance requirement. In: Proceedings of the 18th international conference on autonomous agents and multiagent systems, pp 1461–1469
Feigenbaum I, Sethuraman J (2015) Strategyproof mechanisms for one-dimensional hybrid and obnoxious facility location models. In: Workshop on incentive and trust in e-communities at the 29th AAAI conference on artificial intelligence, pp 8–13
Fong K, Li M, Lu P, Todo T, Yokoo T (2018) Facility lcation games with fractional preferences. In: Proceedings of the 32nd AAAI conference on artificial intelligence, pp 1039–1046
Fotakis D, Tzamos C (2014) On the power of deterministic mechanisms for facility location games. ACM Trans Econ Comput 2(4), Article 15
Groves T (1973) Incentive in teams. Econometrica 41(4):617–631
Li M, Lu P, Yao Y, Zhang J (2020) Strategyproof mechanism for two heterogeneous facilities with constant approximation ratio. In: Proceedings of the 29th international joint conference on artificial intelligence, pp 238–245. https://doi.org/10.24963/ijcai.2020/34
Lipton R, Markakis E, Mossel E, Saberi A (2004) On approximately fair allocations of indivisible goods. In: Proceedings of the 5th ACM conference on electronic commerce, pp 125–131
Lu P, Wang Y, Zhou Y (2009) Tighter bounds for facility games. In: Proceedings of the 5th international workshop on internet and network economics, pp 137–148
Lu P, Sun X, Wang Y, Zhu Z (2010) Asymptotically optimal strategy-proof mechanisms for two-facility games. In: Proceedings of the 11th ACM conference on electronic commerce, 315–324
Mei L, Li M, Ye D, Zhang G (2019) Facility location games with distinct desires. Discrete Appl Math 264:148–160
Moulin H (1980) On strategy-proofness and single peakedness. Public Choice 35(4):437–455
Nguyen TT, Rothe J (2013) How to decrease the degree of envy in allocations of indivisible goods. In: Proceedings of the 3rd international conference on algorithmic decision theory, pp 271–284
Nisan N, Ronen A (2001) Algorithmic mechanism design. Games Econ Behav 35:166–196
Procaccia AD, Tennenholtz M (2009) Approximate mechanism design without money. In: Proceedings of the 10th ACM conference on electronic commerce, pp 177–186
Schummer J, Vohra R (2007) Mechanism design without money. In: Nisan N, Roughgarden T, Tardos É, Vazirani V (eds) Algorithmic Game Theory. Cambridge University Press, New York, pp 243–266
Serafino P, Ventre C (2016) Heterogeneous facility location without money. Theor Comput Sci 636:27–46
Vickrey W (1961) Counterspeculation, auctions and competitive sealed tenders. J Finance 16:8–37
Wada Y, Ono T, Todo T, Yokoo M (2018) Facility location with variable and dynamic populations. In: Proceedings of the 10th international conference on autonomous agents and multiagent systems, pp 336–344
Yuan H, Wang K, Fong K, Zhang Y, Li M (2016) Facility location games with optional preference. In: Proceedings of the twenty-second european conference on artificialintelligence, pp 1520–1527
Zhang Q, Li M (2014) Strategyproof mechanism design for facility location games with weighted agents on a line. J Comb Optim 28(4):756–773. https://doi.org/10.1007/s10878-013-9598-8
Zou S, Li M (2015) Facility location games with dual preference. In: Proceedings of the 14th international conference on autonomous agents and multiagent systems, pp 615–623
This research was supported partially by the National Natural Science Foundation of China (11971447, 11871442), the Natural Science Foundation of Shandong Province of China (ZR2019MA052) and the Fundamental Research Funds for the Central Universities of China (201964006, 201861001).
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A preliminary version of this paper appeared in the Proceedings of the 14th International Conference on Algorithmic Aspects in Information and Management (AAIM 2020), Z. Zhang et al. (Eds.), Lecture Notes in Computer Science 12290, Springer, 260–272.
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Chen, X., Fang, Q., Liu, W. et al. Strategyproof mechanisms for 2-facility location games with minimax envy. J Comb Optim (2021). https://doi.org/10.1007/s10878-021-00711-7
- Facility location game
- Mechanism design
- Maximum envy