On the Power of Deterministic Mechanisms for Facility Location Games
We investigate the approximability of K-Facility Location by deterministic strategyproof mechanisms. Our main result is an elegant characterization of deterministic strategyproof mechanisms with a bounded approximation ratio for 2-Facility Location on the line. Specifically, we show that for instances with n ≥ 5 agents, any such mechanism either admits a unique dictator, or always places the facilities at the two extremes. As a consequence, we obtain that the best approximation ratio achievable by deterministic strategyproof mechanisms for 2-Facility Location on the line is precisely n − 2. Employing a technical tool developed for the characterization, we show that for every K ≥ 3, there do not exist any deterministic anonymous strategyproof mechanisms with a bounded approximation ratio for K-Facility Location on the line, even for simple instances with K + 1 agents. Moreover, building on the characterization for the line, we show that there do not exist any deterministic mechanisms with a bounded approximation ratio for 2-Facility Location in more general metric spaces, which is true even for simple instances with 3 agents located in a star.
Unable to display preview. Download preview PDF.
- 4.Dokow, E., Feldman, M., Meir, R., Nehama, I.: Mechanism design on discrete lines and cycles. In: Proc. of the 13th ACM Conf. on Electronic Commerce (EC 2012), pp. 423–440 (2012)Google Scholar
- 5.Escoffier, B., Gourvès, L., Thang, N.K., Pascual, F., Spanjaard, O.: Strategy-proof mechanisms for facility location games with many facilities. In: Brafman, I., Roberts, F., Tsoukiás, A. (eds.) ADT 2011. LNCS (LNAI), vol. 6992, pp. 67–81. Springer, Heidelberg (2011)Google Scholar
- 6.Feldman, M., Wilf, Y.: Strategyproof Facility Location and the least squares objective. In: Proc. of the 14th ACM Conference on Electronic Commerce, EC 2013 (2013)Google Scholar
- 7.Fotakis, D., Tzamos, C.: Strategyproof Facility Location with concave costs. In: Proc. of the 14th ACM Conference on Electronic Commerce, EC 2013 (2013)Google Scholar
- 11.Lu, P., Sun, X., Wang, Y., Zhu, Z.A.: Asymptotically optimal strategyproof mechanisms for Two-Facility Games. In: Proc. of the 11th ACM Conf. on Electronic Commerce (EC 2010), pp. 315–324 (2010)Google Scholar
- 15.Nissim, K., Smorodinsky, R., Tennenholtz, M.: Approximately optimal mechanism design via Differential Privacy. In: Proc. of the 3rd Conference on Innovations in Theoretical Computer Science (ITCS 2012), pp. 203–213 (2012)Google Scholar
- 16.Procaccia, A.D., Tennenholtz, M.: Approximate mechanism design without money. In: Proc. of the 10th ACM Conference on Electronic Commerce (EC 2009), pp. 177–186 (2009)Google Scholar