Abstract
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 and sum-dist cost. We are interested in investigating strategyproof mechanisms for 2-facility location games in both cases.
In the case of min-dist personal cost, we prove that a lower bound of the additive approximation for any deterministic strategyproof mechanism is 1/4; then we propose a 1/2-additive approximate deterministic group strategyproof mechanism and a 1/4-additive approximate randomized strategyproof mechanism. In the case of sum-dist personal cost, we design an optimal and group strategyproof deterministic mechanism.
This research was supported partially by the National Natural Science Foundation of China (11871442, 11971447) and the Fundamental Research Funds for the Central Universities (201964006, 201861001).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alon, N., Shapira, A., Sudakov, B.: Additive approximation for edge-deletion problems. Ann. Math. 170(1), 371–411 (2009)
Ben-Porat, O., Tennenholtz, M.: Multiunit facility location games. Math. Oper. Res. 44(3), 865–889 (2019)
Cai, Q., Filos-Ratsikas A., Tang, P.: Facility location with minimax envy. In: Proceedings of the 25th International Joint Conference on Artificial Intelligence, pp. 137–143 (2016)
Cheng, Y., Yu, W., Zhang, G.: Mechanisms for obnoxious facility game on a path. In: Wang, W., Zhu, X., Du, D.-Z. (eds.) COCOA 2011. LNCS, vol. 6831, pp. 262–271. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22616-8_21
Duan, L., Li, B., Li, M., Xu, X.: Heterogeneous two-facility location games with minimum distance requirement. In: Proceedings of the 18th International Conference on Autonomous Agents and MultiAgent Systems, pp. 1461–1469 (2019)
Fong, K., Li, M., Lu, P., Todo, T., Yokoo, T.: Facility location games with fractional preferences. In: Proceedings of the 32nd AAAI Conference on Artificial Intelligence, pp. 1039–1046 (2018)
Fotakis, D., Tzamos, C.: On the power of deterministic mechanisms for facility location games. ACM Trans. Econ. Comput. 2(4), 1–37 (2014). Article 15
Lipton, R., Markakis, E., Mossel, E., Saberi, A.: On approximately fair allocations of indivisible goods. In: Proceedings of the 5th ACM Conference on Electronic Commerce, pp. 125–131 (2004)
Li, M., Lu, P., Yao, Y., Zhang, J.: Strategyproof mechanism for two heterogeneous facilities with constant approximation ratio. In: Proceedings of the International Joint Conference on Artificial Intelligence (2020)
Lu, P., Sun, X., Wang, Y., Zhu, Z.: Asymptotically optimal strategy-proof mechanisms for two-facility games. In: Proceedings of the 11th ACM Conference on Electronic Commerce, pp. 315–324 (2010)
Lu, P., Wang, Y., Zhou, Y.: Tighter bounds for facility games. In: Leonardi, S. (ed.) WINE 2009. Lecture Notes in Computer Science, vol. 5929, pp. 137–148. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10841-9_14
Mei, L., Li, M., Ye, D., Zhang, G.: Facility location games with distinct desires. Discrete Appl. Math. 264, 148–160 (2019)
Miyagawa, E.: Locating libraries on a street. Soc. Choice Welfare 18, 527–541 (2001). https://doi.org/10.1007/s003550000074
Moulin, H.: On strategy-proofness and single peakedness. Public Choice 35(4), 437–455 (1980). https://doi.org/10.1007/BF00128122
Nguyen, T.T., Rothe, J.: How to decrease the degree of envy in allocations of indivisible goods. In: Perny, P., Pirlot, M., Tsoukiàs, A. (eds.) ADT 2013. LNCS (LNAI), vol. 8176, pp. 271–284. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-41575-3_21
Nisan, N., Ronen, A.: Algorithmic mechanism design. Games Econ. Behav. 35, 166–196 (2001)
Procaccia, A.D., Tennenholtz, M.: Approximate mechanism design without money. In: Proceedings of the 10th ACM Conference on Electronic Commerce, pp. 177–186 (2009)
Wada, Y., Ono, T., Todo, T., Yokoo, M.: Facility location with variable and dynamic populations. In: Proceedings of the 10th International Conference on Autonomous Agents and Multiagent Systems, pp. 336–344 (2018)
Yuan, H., Wang, K., Fong, K., Zhang, Y., Li, M.: Facility location games with optional preference. In: Proceedings of the Twenty-Second European Conference on Artificial Intelligence, pp. 1520–1527 (2016)
Zou, S., Li, M.: Facility location games with dual preference. In: Proceedings of the 14th International Conference on Autonomous Agents and Multiagent Systems, pp. 615–623 (2015)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Chen, X., Fang, Q., Liu, W., Ding, Y. (2020). Strategyproof Mechanisms for 2-Facility Location Games with Minimax Envy. In: Zhang, Z., Li, W., Du, DZ. (eds) Algorithmic Aspects in Information and Management. AAIM 2020. Lecture Notes in Computer Science(), vol 12290. Springer, Cham. https://doi.org/10.1007/978-3-030-57602-8_24
Download citation
DOI: https://doi.org/10.1007/978-3-030-57602-8_24
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-57601-1
Online ISBN: 978-3-030-57602-8
eBook Packages: Computer ScienceComputer Science (R0)