Skip to main content
SpringerLink
Log in

Strategyproof Facility Location for Three Agents on a Circle

  • Conference paper
  • First Online:
Algorithmic Game Theory (SAGT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 11801))

Included in the following conference series:

Abstract

We consider the facility location problem in a metric space, focusing on the case of three agents. We show that selecting the reported location of each agent with probability proportional to the distance between the other two agents results in a mechanism that is strategyproof in expectation, and dominates the random dictator mechanism in terms of utilitarian social welfare. We further improve the upper bound for three agents on a circle to \(\frac{7}{6}\) (whereas random dictator obtains \(\frac{4}{3}\)); and provide the first lower bounds for randomized strategyproof facility location in any metric space, using linear programming.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 74.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Alon et al. [1] proposed a randomized strategyproof mechanism specifically for circles, called the hybrid mechanism. They showed that it obtains the best possible approximation ratio for the minimax cost, yet for the social cost it achieves a poor approximation ratio of \(\frac{n-1}{2}\).

  2. 2.

    We verified this with Wolfram Alpha.

  3. 3.

    Note that using the reciprocal of the social cost (as in [10]) would lead to a poor outcome in the single facility problem.

  4. 4.

    A mechanism is neutral if it is invariant to renaming of vertices, and anonymous if it is invariant to renaming of agents.

References

  1. Alon, N., Feldman, M., Procaccia, A.D., Tennenholtz, M.: Strategyproof approximation of the minimax on networks. Math. Oper Res. 35(3), 513–526 (2010)

    Article  MathSciNet  Google Scholar 

  2. Alon, N., Feldman, M., Procaccia, A.D., Tennenholtz, M.: Walking in circles. Discrete Math. 310(23), 3432–3435 (2010)

    Article  MathSciNet  Google Scholar 

  3. Anastasiadis, E., Deligkas, A.: Heterogeneous facility location games. In: Proceedings of 17th AAMAS, pp. 623–631, 2018

    Google Scholar 

  4. Anshelevich, E., Postl, J.: Randomized social choice functions under metric preferences. J. Artif. Intell. Res. 58, 797–827 (2017)

    Article  MathSciNet  Google Scholar 

  5. Black, D.: On the rationale of group decision-making. J. Polit. Econ. 56(1), 23–34 (1948)

    Article  Google Scholar 

  6. Cai, Q., Filos-Ratsikas, A., Tang, P.: Facility location with minimax envy. In: Proceedings of 25th IJCAI (2016)

    Google Scholar 

  7. Caragiannis, I., Kalaitzis, D., Markakis, E.: Approximation algorithms and mechanism design for minimax approval voting. In: Proceedings of 24th AAAI (2010)

    Google Scholar 

  8. Conitzer, V., Sandholm, T.: Complexity of mechanism design. In: Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence, pp. 103–110. Morgan Kaufmann Publishers Inc. (2002)

    Google Scholar 

  9. Dokow, E., Feldman, M., Meir, R., Nehama, I.: Mechanism design on discrete lines and cycles. In: Proceedings of 13th ACM-EC, pp. 423–440 (2012)

    Google Scholar 

  10. Escoffier, B., Gourvès, L., Kim Thang, N., Pascual, F., Spanjaard, O.: Strategy-proof mechanisms for facility location games with many facilities. In: Brafman, R.I., Roberts, F.S., Tsoukiàs, A. (eds.) ADT 2011. LNCS (LNAI), vol. 6992, pp. 67–81. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-24873-3_6

    Chapter  Google Scholar 

  11. Feldman, M., Fiat, A., Golomb, I.: On voting and facility location. In: Proceedings of the 2016 ACM Conference on Economics and Computation, pp. 269–286. ACM (2016)

    Google Scholar 

  12. Feldman, M., Wilf, Y.: Strategyproof facility location and the least squares objective. In: Proceedings of 14th ACM-EC, pp. 873–890 (2013)

    Google Scholar 

  13. Filos-Ratsikas, A., Li, M., Zhang, J., Zhang, Q.: Facility location with double-peaked preferences. Auton. Agents Multi-agent Syst. 31(6), 1209–1235 (2017)

    Article  Google Scholar 

  14. Florez, J.V., Lauras, M., Okongwu, U., Dupont, L.: A decision support system for robust humanitarian facility location. Eng. Appl. Artif. Intell. 46, 326–335 (2015)

    Article  Google Scholar 

  15. Golowich, N., Narasimhan, H., Parkes, D.C.: Deep learning for multi-facility location mechanism design. In: IJCAI, pp 261–267 (2018)

    Google Scholar 

  16. Guo, M., Conitzer, V.: Computationally feasible automated mechanism design: general approach and case studies. In: AAAI, vol. 10, pp. 1676–1679 (2010)

    Google Scholar 

  17. Kalai, E., Muller, E.: Characterization of domains admitting nondictatorial social welfare functions and nonmanipulable voting procedures. J. Econ. Theory 16, 457–469 (1977)

    Article  MathSciNet  Google Scholar 

  18. 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, pp. 315–324. ACM (2010)

    Google Scholar 

  19. Mei, L., Li, M., Ye, D., Zhang, G.: Strategy-proof mechanism design for facility location games: revisited. In: Proceedings of 15th AAMAS, pp. 1463–1464 (2016)

    Google Scholar 

  20. Meir, R.: Strategic voting. Synth. Lect. Artif. Intell. Mach. Learn. 13(1), 1–167 (2018). Morgan & Claypool Publishers

    MathSciNet  Google Scholar 

  21. Meir, R.: Strategyproof facility location for three agents on a circle. arXiv preprint arXiv:1902.08070 (2019)

  22. Meir, R., Almagor, S., Michaely, A., Rosenschein, J.S.: Tight bounds for strategyproof classification. In: Proceedings of 10th AAMAS, pp. 319–326 (2011)

    Article  Google Scholar 

  23. Meir, R., Procaccia, A.D., Rosenschein, J.S.: Algorithms for strategyproof classification. Artif. Intell. 186, 123–156 (2012)

    Article  MathSciNet  Google Scholar 

  24. Moujahed, S., Simonin, O., Koukam, A., Ghédira, K.: A reactive agent based approach to facility location: application to transport. In: 4th Workshop on Agants in Traffic and Transportation, located at Autonomous Agents and Multiagent Systems (AAMAS 2006), pp. 63–69, Citeseer (2006)

    Google Scholar 

  25. Moulin, H.: On strategy-proofness and single-peakedness. Public Choice 35, 437–455 (1980)

    Article  Google Scholar 

  26. Narasimhan, H., Agarwal, S., Parkes, D.C.: Automated mechanism design without money via machine learning. In: Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence, pp. 433–439. AAAI Press (2016)

    Google Scholar 

  27. Nehring, K., Puppe, C.: The structure of strategy-proof social choice - part I: general characterization and possibility results on median spaces. J. Econ. Theory 135(1), 269–305 (2007)

    Article  MathSciNet  Google Scholar 

  28. Procaccia, A.D., Tennenholtz, M.: Approximate mechanism design without money. In: Proceedings of the 10th ACM conference on Electronic commerce, pp. 177–186. ACM (2009)

    Google Scholar 

  29. Procaccia, A.D., Tennenholtz, M.: Approximate mechanism design without money. ACM Trans. Econ. Comput. (TEAC) 1(4), 18 (2013)

    Google Scholar 

  30. Schummer, J., Vohra, R.V.: Strategy-proof location on a network. J. Econ. Theory 104(2), 405–428 (2004)

    Article  MathSciNet  Google Scholar 

  31. Serafino, P., Ventre, C.: Truthful mechanisms without money for non-utilitarian heterogeneous facility location. In: Proceedings of 29th AAAI, pp. 1029–1035, (2015)

    Google Scholar 

  32. Sui, X., Boutilier, C.: Approximately strategy-proof mechanisms for (constrained) facility location. In: Proceedings of 14th AAMAS, pp. 605–613 (2015)

    Google Scholar 

  33. Todo, T., Iwasaki, A., Yokoo, M.: False-name-proof mechanism design without money. In: Proceedings of 10th AAMAS, pp. 651–658 (2011)

    Google Scholar 

  34. Zou, A., Li, M.: Facility location games with dual preference. In: Proceedings of 14th AAMAS, pp. 615–623 (2015)

    Google Scholar 

Download references

Acknowledgments

This work was supported in part thanks to the Israeli Science Foundation grant number 773/16.

Author information

Authors and Affiliations

  1. Technion—Israel Institute of Technology, Haifa, Israel

    Reshef Meir

Authors
  1. Reshef Meir
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Reshef Meir .

Editor information

Editors and Affiliations

  1. National Technical University of Athens, Athens, Greece

    Dimitris Fotakis

  2. Athens University of Economics and Business, Athens, Greece

    Evangelos Markakis

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Meir, R. (2019). Strategyproof Facility Location for Three Agents on a Circle. In: Fotakis, D., Markakis, E. (eds) Algorithmic Game Theory. SAGT 2019. Lecture Notes in Computer Science(), vol 11801. Springer, Cham. https://doi.org/10.1007/978-3-030-30473-7_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-30473-7_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-30472-0

  • Online ISBN: 978-3-030-30473-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation