Abstract
In this paper, we study the (group) strategy-proofness of deterministic mechanisms in the obnoxious facility game. In this game, given a set of strategic agents in a metric, we design a mechanism that outputs the location of a facility in the metric based on the locations of the agents reported by themselves. The benefit of an agent is the distance between her location and the facility and the social benefit is the total benefits of all agents. An agent may try to manipulate outputs by the mechanism by misreporting strategically her location. We wish to design a mechanism that is strategy-proof (i.e., no agent can gain her benefit by misreporting) or group strategy-proof (i.e., there is no coalition of agents such that each member in the coalition can simultaneously gain benefit by misreporting), while the social benefit will be maximized. In this paper, we first prove that, in the line metric, there is no strategy-proof mechanism such that the number of candidates (locations output by the mechanism for some reported locations) is more than two. We next completely characterize (group) strategy-proof mechanisms with exactly two candidates in the general metric and show that there exists a 4-approximation group strategy-proof mechanism in any metric.
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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)
Black, D.: On the rationale of group decision-making. Journal of Political Economy 56, 23–34 (1948)
Border, K.C., Jordan, J.S.: Straightforward elections, unanimity and phantom voters. The Review of Economic Studies 50(1), 153–170 (1983)
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)
Church, R.L., Garfinkel, R.S.: Locating an obnoxious facility on a network. Transportation Science 12(2), 107–118 (1978)
Jain, K., Mahdian, M.: Cost sharing. In: Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V. (eds.) Algorithmic Game Theory, ch. 15. Cambridge University Press (2007)
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)
Lu, P., Sun, X., Wang, Y., Zhu, Z.A.: Asymptotically optimal strategy-proof mechanisms for two-facility games. In: Proceedings of the 11th ACM Conference on Electronic Commerce, ACM-EC (June 2010)
Moulin, H.: On strategy proofness and single peakedness. Public Choice 35, 437–455 (1980)
Procaccia, A.D., Tennenholtz, M.: Approximate mechanism design without money. In: Proceedings of the 10th ACM Conference on Electronic Commerce, ACM-EC (July 2009)
Schummer, J., Vohra, R.V.: Strategy-proof location on a network. Journal of Economic Theory 104(2), 405–428 (2004)
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 (2007)
Zelinka, B.: Medians and peripherians of trees. Archivum Mathematicum 4, 87–95 (1968)
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Ibara, K., Nagamochi, H. (2012). Characterizing Mechanisms in Obnoxious Facility Game. In: Lin, G. (eds) Combinatorial Optimization and Applications. COCOA 2012. Lecture Notes in Computer Science, vol 7402. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31770-5_27
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DOI: https://doi.org/10.1007/978-3-642-31770-5_27
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