Abstract
We consider a new facility game, namely, an obnoxious facility game where the facility is undesirable and all agents try to be as far away from the facility as possible. The social cost is the total distance between the agents and the facility. However, an obnoxious facility is placed based on the reported locations of the selfish agents. We are interested in a mechanism to decide the facility location so that the social cost is maximized. In this paper, we give a first attempt for this game on a path. Our main results include a 3-approximation group strategy-proof deterministic mechanism, which is best possible if the facility can only take one of the endpoints on the path, and two group strategy-proof randomized mechanisms with approximation ratio of \(\frac{5}{3}\) and \(\frac{3}{2}\), respectively.
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References
Alon, N., Feldman, M., Procaccia, A.D., Tennenholtz, M.: Strategyproof approximation mechanisms for location on networks. CoRR, abs/0907.2049 (2009)
Church, R.L., Garfinkel, R.S.: Locating an obnoxious facility on a network. Transp. Sci. 12, 107–118 (1978)
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, (ACM-EC) (2010)
Lu, P., Wang, Y., Zhou, Y.: Tighter bounds for facility games. In: Leonardi, S. (ed.) WINE 2009. LNCS, vol. 5929, pp. 137–148. Springer, Heidelberg (2009)
Nisan, N.: Introduction to mechanism design (for computer scientists). In: Nisan, N., Roughgarden, T., Tardos, É., Vazirani, V. (eds.) Algorithmic Game Theory. ch.9. Cambridge University Press, Cambridge
Procaccia, A.D., Tennenholtz, M.: Approximate mechanism design without money. In: Proceedings of the 10th ACM Conference on Electronic Commerce, (ACM-EC) (2009)
Schummer, J., Vohra, R.V.: Mechanism design without money. In: Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V. (eds.) Algorithmic Game Theory. ch.10. Cambridge University Press, Cambridge (2007)
Tamir, A.: Obnoxious facility location on graphs. SIAM Journal on Discrete Mathematics 4, 550–567 (1991)
Ting, S.S.: A linear-time algorithm for maxisum facility location on tree networks. Transp. Sci. 18, 76–84 (1984)
Zelinka, B.: Medians and peripherians of trees. Arch. Math. 4, 87–95 (1968)
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Cheng, Y., Yu, W., Zhang, G. (2011). Mechanisms for Obnoxious Facility Game on a Path. In: Wang, W., Zhu, X., Du, DZ. (eds) Combinatorial Optimization and Applications. COCOA 2011. Lecture Notes in Computer Science, vol 6831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22616-8_21
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DOI: https://doi.org/10.1007/978-3-642-22616-8_21
Publisher Name: Springer, Berlin, Heidelberg
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