Skip to main content

The Price of Anarchy of the Proportional Allocation Mechanism Revisited

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNISA,volume 8289)

Abstract

We consider the proportional allocation mechanism first studied by Kelly (1997) in the context of congestion control algorithms for communication networks. A single infinitely divisible resource is to be allocated efficiently to competing players whose individual utility functions are unknown to the resource manager. If players anticipate the effect of their bids on the price of the resource and their utility functions are concave, strictly increasing and continuously differentiable, Johari and Tsitsiklis (2004) proved that the price of anarchy is 4/3. The question was raised whether there is a relationship between this result and that of Roughgarden and Tardos (2002), who had earlier shown exactly the same bound for nonatomic selfish routing with affine-linear congestion functions. We establish such a relationship and show, in particular, that the efficiency loss can be characterized by precisely the same geometric quantity. We also present a new variational inequality characterization of Nash equilibria in this setting, which enables us to extend the price-of-anarchy analysis to important classes of utility functions that are not necessarily concave.

Keywords

  • Utility Function
  • Nash Equilibrium
  • Variational Inequality
  • Geometric Quantity
  • Congestion Game

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-642-45046-4_10
  • Chapter length: 12 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   59.99
Price excludes VAT (USA)
  • ISBN: 978-3-642-45046-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   74.99
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Correa, J.R., Schulz, A.S., Stier-Moses, N.E.: Selfish routing in capacitated networks. Mathematics of Operations Research 29, 961–976 (2004)

    MathSciNet  CrossRef  MATH  Google Scholar 

  2. Correa, J.R., Schulz, A.S., Stier-Moses, N.E.: A geometric approach to the price of anarchy in nonatomic congestion games. Games and Economic Behavior 64, 457–469 (2008)

    MathSciNet  CrossRef  MATH  Google Scholar 

  3. Hajek, B., Gopalakrishnan, G.: Do greedy autonomous systems make for a sensible Internet? Presented at the Conference on Stochastic Networks, Stanford University, CA (2002)

    Google Scholar 

  4. Johari, R.: The price of anarchy and the design of scalable resource allocation mechanisms. In: Nisan, N., Roughgarden, T., Tardos, É., Vazirani, V.V. (eds.) Algorithmic Game Theory. Cambridge University Press (2007)

    Google Scholar 

  5. Johari, R., Tsitsiklis, J.N.: Efficiency loss in a network resource allocation game. Mathematics of Operations Research 29, 407–435 (2004)

    MathSciNet  CrossRef  MATH  Google Scholar 

  6. Kelly, F.: Charging and rate control for elastic traffic. European Transactions on Telecommunications 8, 33–37 (1997)

    CrossRef  Google Scholar 

  7. Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)

    CrossRef  Google Scholar 

  8. Roughgarden, T.: The price of anarchy is independent of the network topology. Journal of Computer and System Sciences 67, 341–364 (2003)

    MathSciNet  CrossRef  MATH  Google Scholar 

  9. Roughgarden, T., Tardos, É.: How bad is selfish routing? Journal of the ACM 49, 236–259 (2002)

    MathSciNet  CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Correa, J.R., Schulz, A.S., Stier-Moses, N.E. (2013). The Price of Anarchy of the Proportional Allocation Mechanism Revisited. In: Chen, Y., Immorlica, N. (eds) Web and Internet Economics. WINE 2013. Lecture Notes in Computer Science, vol 8289. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45046-4_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-45046-4_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45045-7

  • Online ISBN: 978-3-642-45046-4

  • eBook Packages: Computer ScienceComputer Science (R0)