Abstract
We study the obnoxious facility game with service range on a path where each facility is undesirable and has service radius r. In this game there are a number of agents on a path. Each agent tries to be far away from all facilities, but still to be served by a facility. Namely, the distance between an agent and her nearest facility is at most r. The utility of an agent is thus defined as this distance. In a deterministic or randomized mechanism, based on the addresses reported by the selfish agents, the locations or the location distributions of facilities are determined. The aim of the mechanisms is to maximize the obnoxious social welfare, the total utilities of all agents. The objective of each agent is to maximize her own utility and she may lie if, by doing so, more benefit can be obtained. We are interested in mechanisms without money to decide the facility locations so that the obnoxious social welfare is maximized and all agents are enforced to report their true locations (strategy-proofness or group strategy-proofness).
In this paper, we give the first attempt for this game on a path to design a group strategy-proof deterministic and randomized mechanism when the service radius \(\frac12\leq r\leq 1\) by assuming that the path length is one. Depending on the value r, we provide different mechanisms with provable approximation ratios. Lower bounds on any deterministic strategy-proof mechanism are also presented.
Research was partially supported by the National Nature Science Foundation of China (No. 11271009, 11271325) and the Nature Science Foundation of Zhejiang Province (No. LQ12A01011).
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References
Alon, N., Feldman, M., Procaccia, A., Tennenholtz, M.: Strategyproof Approximation Mechanisms for Location on Networks, Computing Research Repository-CORR, abs/0907.2049 (2009)
Alon, N., Feldman, M., Procaccia, A., Tennenholtz, M.: Strategyproof Approximation of the Minimax on Networks. Mathematics of Operations Research 35, 513–526 (2010)
Cheng, Y., Yu, W., Zhang, G.: Strategy-proof Approximation Mechanisms for an Obnoxious Facility Game on Networks. Theoretical Computer Science (2011), doi: 10.1016/j.tcs.2011.11.041
Escoffier, B., Gourvès, L., Thang, N.K., Pascual, F., Spanjaard, O.: Strategy-Proof Mechanisms for Facility Location Games with Many Facilities. In: Brafman, R. (ed.) ADT 2011. LNCS, vol. 6992, pp. 67–81. Springer, Heidelberg (2011)
Fotakis, D., Tzamos, C.: Winner-imposing Strategyproof Mechanisms for Multiple Facility Location Games. In: Saberi, A. (ed.) WINE 2010. LNCS, vol. 6484, pp. 234–245. Springer, Heidelberg (2010)
Ibara, K., Nagamochi, H.: Characterizing Mechanisms in Obnoxious Facility Game. In: Lin, G. (ed.) COCOA 2012. LNCS, vol. 7402, pp. 301–311. Springer, Heidelberg (2012)
Han, Q., Du, D.: Moneyless Strategy-proof Mechanism on Single-sinked Policy Domain: Characerization and Applications (2012) (working paper)
Lu, P., Sun, X., Wang, Y., Zhu, Z.: Asymptotically Optimal Strategy-proof Mechanisms for Two-facility Games. In: 11th ACM Conference on Electronic Commerce, pp. 315–324. ACM, New York (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)
Moulin, H.: On strategy-proofness and single peakedness. Public Choice 35(4), 437–455 (1980)
Procaccia, A., Tennenholtz, M.: Approximate mechanism design without money. In: 10th ACM Conference on Electronic Commerce (ACM-EC), pp. 177–186. ACM, New York (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 (2007)
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Cheng, Y., Han, Q., Yu, W., Zhang, G. (2013). Obnoxious Facility Game with a Bounded Service Range. In: Chan, TH.H., Lau, L.C., Trevisan, L. (eds) Theory and Applications of Models of Computation. TAMC 2013. Lecture Notes in Computer Science, vol 7876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38236-9_25
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DOI: https://doi.org/10.1007/978-3-642-38236-9_25
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