Skip to main content
SpringerLink
Log in

Cost-Sharing in Generalised Selfish Routing

  • Conference paper
  • First Online:
Book cover Algorithms and Complexity (CIAC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10236))

Included in the following conference series:

Abstract

We study a generalisation of atomic selfish routing games where each player may control multiple flows which she routes seeking to minimise their aggregate cost. Such games emerge in various settings, such as traffic routing in road networks by competing ride-sharing applications or packet routing in communication networks by competing service providers who seek to optimise the quality of service of their customers. We study the existence of pure Nash equilibria in the induced games and we exhibit a separation from the single-commodity per player model by proving that the Shapley value is the only cost-sharing method that guarantees it. We also prove that the price of anarchy and price of stability is no larger than in the single-commodity model for general cost-sharing methods and general classes of convex cost functions. We close by giving results on the existence of pure Nash equilibria of a splittable variant of our model.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

References

  1. Abed, F., Correa, J.R., Huang, C.-C.: Optimal coordination mechanisms for multi-job scheduling games. In: Schulz, A.S., Wagner, D. (eds.) ESA 2014. LNCS, vol. 8737, pp. 13–24. Springer, Heidelberg (2014). doi:10.1007/978-3-662-44777-2_2

    Google Scholar 

  2. Aland, S., Dumrauf, D., Gairing, M., Monien, B., Schoppmann, F.: Exact price of anarchy for polynomial congestion games. SIAM J. Comput. 40(5), 1211–1233 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. Anshelevich, E., Dasgupta, A., Kleinberg, J., Tardos, E., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. SIAM J. Comput. 38(4), 1602–1623 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Awerbuch, B., Azar, Y., Epstein, A.: The price of routing unsplittable flow. In: Proceedings of STOC, pp. 57–66. ACM (2005)

    Google Scholar 

  5. Bhaskar, U., Fleischer, L., Hoy, D., Huang, C.: Equilibria of atomic flow games are not unique. In: Proceedings of SODA, pp. 748–757 (2009)

    Google Scholar 

  6. Bhawalkar, K., Gairing, M., Roughgarden, T.: Weighted congestion games: price of anarchy, universal worst-case examples, and tightness. Proc. of ACM TEAC 2(4), 14 (2014)

    MATH  Google Scholar 

  7. Christodoulou, G., Gairing, M.: Price of stability in polynomial congestion games. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds.) ICALP 2013. LNCS, vol. 7966, pp. 496–507. Springer, Heidelberg (2013). doi:10.1007/978-3-642-39212-2_44

    Chapter  Google Scholar 

  8. Christodoulou, G., Koutsoupias, E.: The price of anarchy of finite congestion games. In: Proceedings of STOC, pp. 67–73. ACM (2005)

    Google Scholar 

  9. Cominetti, R., Correa, J.R., Moses, N.E.S.: The impact of oligopolistic competition in networks. Oper. Res. 57(6), 1421–1437 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Fotakis, D., Kontogiannis, S., Spirakis, P.: Atomic congestion games among coalitions. ACM Trans. Algorithms (TALG) 4(4), 52 (2008)

    MathSciNet  MATH  Google Scholar 

  11. Fotakis, D., Spirakis, P.G.: Cost-balancing tolls for atomic network congestion games. Internet Math. 5(4), 343–363 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Gairing, M., Kollias, K., Kotsialou, G.: Tight bounds for cost-sharing in weighted congestion games. In: Halldórsson, M.M., Iwama, K., Kobayashi, N., Speckmann, B. (eds.) ICALP 2015. LNCS, vol. 9135, pp. 626–637. Springer, Heidelberg (2015). doi:10.1007/978-3-662-47666-6_50

    Chapter  Google Scholar 

  13. Gairing, M., Schoppmann, F.: Total latency in singleton congestion games. In: Deng, X., Graham, F.C. (eds.) WINE 2007. LNCS, vol. 4858, pp. 381–387. Springer, Heidelberg (2007). doi:10.1007/978-3-540-77105-0_42

    Chapter  Google Scholar 

  14. Gkatzelis, V., Kollias, K., Roughgarden, T.: Optimal cost-sharing in weighted congestion games. In: Liu, T.-Y., Qi, Q., Ye, Y. (eds.) WINE 2014. LNCS, vol. 8877, pp. 72–88. Springer, Cham (2014). doi:10.1007/978-3-319-13129-0_6

    Google Scholar 

  15. Gopalakrishnan, R., Marden, J.R., Wierman, A.: Potential games are necessary to ensure pure Nash equilibria in cost sharing games. Math. Oper. Res. 39, 1252–1296 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  16. Harks, T.: Stackelberg strategies and collusion in network games with splittable flow. Theory Comput. Syst. 48(4), 781–802 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. Harks, T., Klimm, M.: On the existence of pure Nash equilibria in weighted congestion games. Math. Oper. Res. 37(3), 419–436 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  18. Harks, T., Klimm, M., Möhring, R.H.: Characterizing the existence of potential functions in weighted congestion games. Theory Comput. Syst. 49(1), 46–70 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  19. Hart, S., Mas-Colell, A.: Potential, value, and consistency. Econom.: J. Econom. Soc. 589–614 (1989)

    Google Scholar 

  20. Hayrapetyan, A., Tardos, É., Wexler, T.: The effect of collusion in congestion games. In: Proceedings of STOC, pp. 89–98 (2006)

    Google Scholar 

  21. Klimm, M., Schmand, D.: Sharing non-anonymous costs of multiple resources optimally. In: Paschos, V.T., Widmayer, P. (eds.) CIAC 2015. LNCS, vol. 9079, pp. 274–287. Springer, Cham (2015). doi:10.1007/978-3-319-18173-8_20

    Chapter  Google Scholar 

  22. Kollias, K., Roughgarden, T.: Restoring pure equilibria to weighted congestion games. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011. LNCS, vol. 6756, pp. 539–551. Springer, Heidelberg (2011). doi:10.1007/978-3-642-22012-8_43

    Chapter  Google Scholar 

  23. Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. Comput. Sci. Rev. 3(2), 65–69 (2009)

    Article  MATH  Google Scholar 

  24. Monderer, D., Shapley, L.S.: Potential games. Games Econ. Behav. 14(1), 124–143 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  25. Orda, A., Rom, R., Shimkin, N.: Competitive routing in multiuser communication networks. IEEE/ACM Trans. Netw. 1(5), 510–521 (1993)

    Article  Google Scholar 

  26. Rosenthal, R.W.: A class of games possessing pure-strategy Nash equilibria. Int. J. Game Theory 2(1), 65–67 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  27. Rosenthal, R.W.: The network equilibrium problem in integers. Networks 3(1), 53–59 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  28. Roughgarden, T.: Intrinsic robustness of the price of anarchy. In: Proceedings of STOC, pp. 513–522. ACM (2009)

    Google Scholar 

  29. Roughgarden, T., Schoppmann, F.: Local smoothness and the price of anarchy in splittable congestion games. J. Econ. Theory 156, 317–342 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  30. Roughgarden, T., Schrijvers, O.: Network cost-sharing without anonymity. In: Lavi, R. (ed.) SAGT 2014. LNCS, vol. 8768, pp. 134–145. Springer, Heidelberg (2014). doi:10.1007/978-3-662-44803-8_12

    Google Scholar 

  31. Roughgarden, T., Tardos, É.: How bad is selfish routing? J. ACM (JACM) 49(2), 236–259 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  32. Sheffi, Y.: Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods. Prentice-Hall, Upper Saddle River (1985)

    Google Scholar 

  33. Tran-Thanh, L., Polukarov, M., Chapman, A., Rogers, A., Jennings, N.R.: On the existence of pure strategy Nash equilibria in integer–splittable weighted congestion games. In: Persiano, G. (ed.) SAGT 2011. LNCS, vol. 6982, pp. 236–253. Springer, Heidelberg (2011). doi:10.1007/978-3-642-24829-0_22

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Liverpool, Liverpool, UK

    Martin Gairing & Grammateia Kotsialou

  2. Stanford University, Stanford, USA

    Konstantinos Kollias

Authors
  1. Martin Gairing
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Konstantinos Kollias
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Grammateia Kotsialou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Grammateia Kotsialou .

Editor information

Editors and Affiliations

  1. National Technical University of Athens, Zografou, Athens, Greece

    Dimitris Fotakis

  2. National Technical University of Athens, Zografou, Athens, Greece

    Aris Pagourtzis

  3. Université Paris-Dauphine, Paris, France

    Vangelis Th. Paschos

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Gairing, M., Kollias, K., Kotsialou, G. (2017). Cost-Sharing in Generalised Selfish Routing. In: Fotakis, D., Pagourtzis, A., Paschos, V. (eds) Algorithms and Complexity. CIAC 2017. Lecture Notes in Computer Science(), vol 10236. Springer, Cham. https://doi.org/10.1007/978-3-319-57586-5_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-57586-5_23

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57585-8

  • Online ISBN: 978-3-319-57586-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation