Skip to main content

Complexity of Pure-Strategy Nash Equilibria in Non-Cooperative Games

  • Conference paper
  • 2361 Accesses

Part of the Operations Research Proceedings book series (ORP,volume 2006)

Abstract

Game theory in general and the concept of Nash equilibrium in particular have lately come under increased scrutiny by theoretical computer scientists. Computing a mixed Nash equilibrium is a case in point. For many years, one of the most important open problems was the complexity of computing a mixed Nash equilibrium in games with only two players. Only recently was it solved by a sequence of significant papers (Goldberg and Papadimitriou (2006), Daskalakis et.al. (2006), Chen and Deng (2005), Daskalakis and Papadimitriou (2005), and Chen and Deng (2006)).

Keywords

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, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anshelevich, E., A. Dasgupta, J. Kleinberg, É. Tardos, T. Wexler, and T. Roughgarden (2004). The price of stability for network design with fair cost allocation. In Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, Rome, Italy, pp. 295–304.

    Google Scholar 

  2. Chen, X. and X. Deng (2005). 3-Nash is PPAD-complete. Electronic Colloquium on Computational Complexity TR05-134.

    Google Scholar 

  3. Chen, X. and X. Deng (2006). Settling the complexity of 2-player Nashequilibrium. In Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science, Berkeley, CA, to appear.

    Google Scholar 

  4. Daskalakis, C., P. Goldberg, and C. Papadimitriou (2006). The complexity of computing a Nash equilibrium. In Proceedings of the 38th Annual ACM Symposium on Theory of Computing, Seattle, WA, pp. 71–78.

    Google Scholar 

  5. Daskalakis, C. and C. Papadimitriou (2005). Three-player games are hard. Electronic Colloquium on Computational Complexity TR05-139.

    Google Scholar 

  6. Dunkel, J. (2005). The Complexity of Pure-Strategy Nash Equilibria in Non-Cooperative Games. Diplomarbeit, Institute of Mathematics, Technische Universität Berlin, Germany, July 2005.

    Google Scholar 

  7. Fotakis, D., S. Kontogiannis, and P. Spirakis (2005). Selfish unsplittable flows. Theoretical Computer Science 348, pp. 226–239.

    CrossRef  Google Scholar 

  8. Goldberg, P. and C. Papadimitriou (2006). Reducibility among equilibrium problems. In Proceedings of the 38th Annual ACM Symposium on Theory of Computing, Seattle, WA, pp. 61–70.

    Google Scholar 

  9. Leyton-Brown, K. and M. Tennenholtz (2003). Local-effect games. In Proceedings of the 18th International Joint Conference on Artificial Intelligence, Acapulco, Mexico, pp. 772–780.

    Google Scholar 

  10. Nash, J. (1951). Non-cooperative games. Annals of Mathematics 54, 268–295.

    CrossRef  Google Scholar 

  11. Rosenthal, R. (1973). A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory 2, pp. 65–67.

    CrossRef  Google Scholar 

  12. Schäffer, A. and M. Yannakakis (1991). Simple local search problems that are hard to solve. SIAM Journal on Computing 20, pp. 56–87.

    CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dunke, J. (2007). Complexity of Pure-Strategy Nash Equilibria in Non-Cooperative Games. In: Waldmann, KH., Stocker, U.M. (eds) Operations Research Proceedings 2006. Operations Research Proceedings, vol 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69995-8_7

Download citation

Publish with us

Policies and ethics