Skip to main content
SpringerLink
Log in

Price of anarchy in machine load balancing game

  • Mathematical Game Theory and Applications
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

This paper considers the machine load balancing game with uniformly related machines. Players choose machines of different speeds to run their jobs striving to minimize job’s delay, i.e., the job completion time on a chosen machine. The social cost is the maximum delay over all machines. In the general case and the special case of 3 machines, we obtain upper estimates for the price of anarchy (PoA) and demonstrate when they coincide with the exact values. Moreover, sufficient conditions for PoA increase are established under new machine inclusion into the system. And finally, we propose a computing algorithm of the exact PoA value in the three-machine model.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Andelman, N., Feldman, M., and Mansour, Y., Strong Price of Anarchy, Proc. 18th Annual ACM–SIAM Symp. on Discrete Algorithms (SODA’07), 2007, pp. 189–198.

    Google Scholar 

  2. Czumaj, A. and Vöcking, B., Tight Bounds for Worst-Case Equilibria, Proc. 13th Annual ACM-SIAM Symp. on Discrete Algorithms (SODA’02), 2002, pp. 413–420.

    Google Scholar 

  3. Epstein, L., Equilibria for Two Parallel Links: The Strong Price of Anarchy Versus the Price of Anarchy, Acta Inform., 2010, vol. 47, nos. 7–8, pp. 375–389.

    Article  MATH  MathSciNet  Google Scholar 

  4. Even-Dar, E., Kesselman, A., and Mansour, Y., Convergence Time to Nash Equilibria, Proc. 30th Int. Colloquium on Automata, Languages and Programming (ICALP2003), 2003, pp. 502–513.

    Chapter  Google Scholar 

  5. Feldmann, R., Gairing, M., Lücking, T., Monien, B., and Rode, M., Nashification and the Coordination Ratio for a Selfish Routing Game, Proc. 30th Int. Colloquium on Automata, Languages and Programming (ICALP2003), 2003, pp. 514–526.

    Chapter  Google Scholar 

  6. Fotakis, D., Kontogiannis, S.C., Koutsoupias, E., Mavronicolas, M., and Spirakis, P.G., The Structure and Complexity of Nash Equilibria for a Selfish Routing Game, Proc. 29th Int. Colloquium on Automata, Languages and Programming (ICALP2002), 2002, pp. 123–134.

    Chapter  Google Scholar 

  7. Korilis, Ya.., Lazar, A.A., and Orda, A., Avoiding the Braess Paradox in Non-Cooperative Networks, J. Appl. Prob., 1999, vol. 36, pp. 211–222.

    Article  MATH  MathSciNet  Google Scholar 

  8. Koutsoupias, E. and Papadimitriou, C.H., Worst-Case Equilibria, Proc. STACS, 1999, vol. 1563, pp. 404–413.

    Article  MathSciNet  Google Scholar 

  9. Lücking, T., Mavronicolas, M., Monien, B., Rode, M., Spirakis, P., and Vrto, I., Which Is the Worst-Case Nash Equilibrium?, Proc. 26th Int. Symp. on Mathematical Foundations of Computer Science, 2003, LNCS 2747, pp. 551–561.

    Google Scholar 

  10. Mazalov, V.V., Mathematical Game Theory and Applications, New York: Wiley, 2014

    MATH  Google Scholar 

  11. Murchland, J.D., Braess’s Paradox of Traffic Flow, Transport. Res., 1970, vol. 4, pp. 391–394.

    Article  Google Scholar 

  12. Roughgarden, T. and Tardos, É., How Bad Is Selfish Routing?, J. ACM, 2002, vol. 49, no. 2, pp. 236–259.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Mathematical Research, Karelian Research Center, Russian Academy of Sciences, Petrozavodsk, Russia

    Yu. V. Chirkova

Authors
  1. Yu. V. Chirkova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu. V. Chirkova.

Additional information

Original Russian Text © Yu.V. Chirkova, 2012, published in Matematicheskaya Teoriya Igr i Priloszheniya, 2012, No. 4, pp. 93–113.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chirkova, Y.V. Price of anarchy in machine load balancing game. Autom Remote Control 76, 1849–1864 (2015). https://doi.org/10.1134/S0005117915100124

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117915100124

Keywords

Search

Navigation