Skip to main content
SpringerLink
Log in

Congestion Games with Mixed Objectives

  • Conference paper
  • First Online:
Combinatorial Optimization and Applications (COCOA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10043))

Abstract

We study a new class of games which generalizes congestion games and its bottleneck variant. We introduce congestion games with mixed objectives to model network scenarios in which players seek to optimize for latency and bandwidths alike. We characterize the existence of pure Nash equilibria (PNE) and the convergence of improvement dynamics. For games that do not possess PNE we give bounds on the approximation ratio of approximate pure Nash equilibria.

This work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Centre “On-The-Fly Computing” (SFB 901) and by the EU within FET project MULTIPLEX under contract no. 317532.

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. Ackermann, H., Röglin, H., Vöcking, B.: Pure nash equilibria in player-specific and weighted congestion games. Theoret. Comput. Sci. 410(17), 1552–1563 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ackermann, H., Röglin, H., Vöcking, B.: On the impact of combinatorial structure on congestion games. J. ACM 55(6), 25:1–25:22 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Ackermann, H., Skopalik, A.: Complexity of pure nash equilibria in player-specific network congestion games. Internet Math. 5(4), 323–342 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Banner, R., Orda, A.: Bottleneck routing games in communication networks. IEEE J. Sel. Areas Commun. 25(6), 1173–1179 (2007)

    Article  Google Scholar 

  5. Caragiannis, I., Fanelli, A., Gravin, N., Skopalik, A.: Efficient computation of approximate pure nash equilibria in congestion games. In: IEEE 52nd Annual Symposium on Foundations of Computer Science (FOCS), pp. 532–541 (2011)

    Google Scholar 

  6. Caragiannis, I., Fanelli, A., Gravin, N., Skopalik, A.: Approximate pure nash equilibria in weighted congestion games: existence, efficient computation, and structure. ACM Trans. Econ. Comput. 3(1), 2:1–2:32 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  7. Chien, S., Sinclair, A.: Convergence to approximate nash equilibria in congestion games. Games Econ. Behav. 71(2), 315–327 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Cole, R., Dodis, Y., Roughgarden, T.: Bottleneck links, variable demand, and the tragedy of the commons. Networks 60(3), 194–203 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  9. Dunkel, J., Schulz, A.S.: On the complexity of pure-strategy nash equilibria in congestion and local-effect games. Math. Oper. Res. 33(4), 851–868 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  10. Feldotto, M., Gairing, M., Skopalik, A.: Bounding the potential function in congestion games and approximate pure nash equilibria. In: Liu, T.-Y., Qi, Q., Ye, Y. (eds.) WINE 2014. LNCS, vol. 8877, pp. 30–43. Springer, Heidelberg (2014). doi:10.1007/978-3-319-13129-0_3

    Google Scholar 

  11. Fotakis, D., Kontogiannis, S., Spirakis, P.: Selfish unsplittable flows. Theoret. Comput. Sci. 348(2), 226–239 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, New York (1979)

    MATH  Google Scholar 

  13. Hansknecht, C., Klimm, M., Skopalik, A.: Approximate pure nash equilibria in weighted congestion games. In: Jansen, K., Rolim, J.D.P., Devanur, N.R., Moore, C. (eds.) Approximation, Randomization, and Combinatorial Optimization, Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), vol. 28, pp. 242–257. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany (2014)

    Google Scholar 

  14. Harks, T., Hoefer, M., Schewior, K., Skopalik, A.: Routing games with progressive filling. IEEE/ACM Trans. Netw. 24(4), 2553–2562 (2016)

    Article  Google Scholar 

  15. Harks, T., Hoefer, M., Klimm, M., Skopalik, A.: Computing pure nash and strong equilibria in bottleneck congestion games. Math. Program. 141(1), 193–215 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  16. Harks, T., Klimm, M., Möhring, R.H.: Strong nash equilibria in games with the lexicographical improvement property. In: Leonardi, S. (ed.) WINE 2009. LNCS, vol. 5929, pp. 463–470. Springer, Heidelberg (2009). doi:10.1007/978-3-642-10841-9_43

    Chapter  Google Scholar 

  17. Mavronicolas, M., Milchtaich, I., Monien, B., Tiemann, K.: Congestion games with player-specific constants. In: Kučera, L., Kučera, A. (eds.) MFCS 2007. LNCS, vol. 4708, pp. 633–644. Springer, Heidelberg (2007). doi:10.1007/978-3-540-74456-6_56

    Chapter  Google Scholar 

  18. Milchtaich, I.: Congestion games with player-specific payoff functions. Games Econ. Behav. 13(1), 111–124 (1996)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  21. Skopalik, A., Vöcking, B.: Inapproximability of pure nash equilibria. In: Proceedings of the Fortieth Annual ACM Symposium on Theory of Computing, STOC 2008, pp. 355–364. ACM, New York (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Heinz Nixdorf Institute & Department of Computer Science, Paderborn University, Paderborn, Germany

    Matthias Feldotto, Lennart Leder & Alexander Skopalik

Authors
  1. Matthias Feldotto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lennart Leder
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alexander Skopalik
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Matthias Feldotto .

Editor information

Editors and Affiliations

  1. University of Hong Kong, Hong Kong, China

    T-H. Hubert Chan

  2. City University of Hong Kong, Hong Kong, China

    Minming Li

  3. City University of Hong Kong, Hong Kong, China

    Lusheng Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing AG

About this paper

Cite this paper

Feldotto, M., Leder, L., Skopalik, A. (2016). Congestion Games with Mixed Objectives. In: Chan, TH., Li, M., Wang, L. (eds) Combinatorial Optimization and Applications. COCOA 2016. Lecture Notes in Computer Science(), vol 10043. Springer, Cham. https://doi.org/10.1007/978-3-319-48749-6_47

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-48749-6_47

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-48748-9

  • Online ISBN: 978-3-319-48749-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation