On the Power of Deterministic Mechanisms for Facility Location Games

  • Dimitris Fotakis
  • Christos Tzamos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7965)

Abstract

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.

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References

  1. 1.
    Alon, N., Feldman, M., Procaccia, A.D., Tennenholtz, M.: Strategyproof approximation of the minimax on networks. Mathematics of Operations Research 35(3), 513–526 (2010)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Barberà, S.: An introduction to strategyproof social choice functions. Social Choice and Welfare 18, 619–653 (2001)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Barberà, S., Beviá, C.: Locating public libraries by majority: Stability, consistency and group formation. Games and Economic Behaviour 56, 185–200 (2006)MATHCrossRefGoogle Scholar
  4. 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. 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. 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. 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
  8. 8.
    Fotakis, D., Tzamos, C.: Winner-imposing strategyproof mechanisms for multiple Facility Location games. Theoretical Computer Science 472, 90–103 (2013)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Ju, B.-G.: Efficiency and consistency for locating multiple public facilities. Journal of Economic Theory 138, 165–183 (2008)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Koutsoupias, E.: Scheduling without payments. In: Persiano, G. (ed.) SAGT 2011. LNCS, vol. 6982, pp. 143–153. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  11. 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
  12. 12.
    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)CrossRefGoogle Scholar
  13. 13.
    Miyagawa, E.: Locating libraries on a street. Social Choice and Welfare 18, 527–541 (2001)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Moulin, H.: On strategy-proofness and single-peakedness. Public Choice 35, 437–455 (1980)CrossRefGoogle Scholar
  15. 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. 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
  17. 17.
    Schummer, J., Vohra, R.V.: Strategyproof location on a network. Journal of Economic Theory 104, 405–428 (2002)MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Schummer, J., Vohra, R.V.: Mechanism design without money. Algorithmic Game Theory 10, 243–299 (2007)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Dimitris Fotakis
    • 1
  • Christos Tzamos
    • 2
  1. 1.School of Electrical and Computer EngineeringNational Technical University of AthensAthensGreece
  2. 2.Computer Science and Artificial Intelligence LaboratoryMassachusetts Institute of TechnologyCambridgeUSA

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