Skip to main content
SpringerLink
Log in

A Unified Framework for Strong Price of Anarchy in Clustering Games

  • Conference paper
  • First Online:
Book cover Automata, Languages, and Programming (ICALP 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9135))

Included in the following conference series:

Abstract

We devise a unified framework for quantifying the inefficiency of equilibria in clustering games on networks. This class of games has two properties exhibited by many real-life social and economic settings: (a) an agent’s utility is affected only by the behavior of her direct neighbors rather than that of the entire society, and (b) an agent’s utility does not depend on the actual strategies chosen by agents, but rather by whether or not other agents selected the same strategy. Our framework is sufficiently general to account for unilateral versus coordinated deviations by coalitions of different sizes, different types of relationships between agents, and different structures of strategy spaces. Many settings that have been recently studied are special cases of clustering games on networks. Using our framework: (1) We recover previous results for special cases and provide extended and improved results in a unified way. (2) We identify new settings that fall into the class of clustering games on networks and establish price of anarchy and strong price of anarchy bounds for them.

This work was partially supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement number 337122.

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andelman, N., Feldman, M., Mansour, Y.: Strong price of anarchy. In: SODA, pp. 189–198 (2007)

    Google Scholar 

  2. Apt, K.R., Rahn, M., Schäfer, G., Simon, S.: Coordination games on graphs (Extended Abstract). In: Liu, T.-Y., Qi, Q., Ye, Y. (eds.) WINE 2014. LNCS, vol. 8877, pp. 441–446. Springer, Heidelberg (2014)

    Google Scholar 

  3. Bachrach, Y., Syrgkanis, V., Tardos, É., Vojnović, M.: Strong price of anarchy, utility games and coalitional dynamics. In: Lavi, R. (ed.) SAGT 2014. LNCS, vol. 8768, pp. 218–230. Springer, Heidelberg (2014)

    Google Scholar 

  4. Banerjee, S., Konishi, H., Sönmez, T.: Core in a simple coalition formation game. Social Choice and Welfare 18(1), 135–153 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bansal, N., Blum, A., Chawla, S.: Correlation clustering. Machine Learning 56(1–3), 89–113 (2004)

    Article  MATH  Google Scholar 

  6. Barberà, S., Gerber, A.: On coalition formation: durable coalition structures. Mathematical Social Sciences 45(2), 185–203 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Bilò, V., Fanelli, A., Flammini, M., Monaco, G., Moscardelli, L.: Nash stability in fractional hedonic games. In: Liu, T.-Y., Qi, Q., Ye, Y. (eds.) WINE 2014. LNCS, vol. 8877, pp. 486–491. Springer, Heidelberg (2014)

    Google Scholar 

  8. Bloch, F., Diamantoudi, E.: Noncooperative formation of coalitions in hedonic games. International Journal of Game Theory 40(2), 263–280 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  9. Bogomolnaia, A., Jackson, M.O.: The stability of hedonic coalition structures. Games and Economic Behavior 38(2), 201–230 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  10. Diamantoudi, E., Xue, L.: Farsighted stability in hedonic games. Social Choice and Welfare 21(1), 39–61 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  11. Dreze, J.H., Greenberg, J.: Hedonic coalitions: Optimality and stability. Econometrica: Journal of the Econometric Society, 987–1003 (1980)

    Google Scholar 

  12. Feldman, M., Lewin-Eytan, L., Naor, J.: Hedonic clustering games. In: SPAA, pp. 267–276. ACM (2012)

    Google Scholar 

  13. Gourvès, L., Monnot, J.: On strong equilibria in the max cut game. In: Leonardi, S. (ed.) WINE 2009. LNCS, vol. 5929, pp. 608–615. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  14. Gourvès, L., Monnot, J.: The max k-cut game and its strong equilibria. In: Kratochvíl, J., Li, A., Fiala, J., Kolman, P. (eds.) TAMC 2010. LNCS, vol. 6108, pp. 234–246. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  15. Hoefer, M.: Cost sharing and clustering under distributed competition. Ph.D thesis, University of Konstanz (2007)

    Google Scholar 

  16. Kearns, M., Littman, M.L., Singh, S.: Graphical models for game theory. In: UAI, pp. 253–260. Morgan Kaufmann Publishers Inc. (2001)

    Google Scholar 

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

    Chapter  Google Scholar 

  18. Kun, J., Powers, B., Reyzin, L.: Anti-coordination games and stable graph colorings. In: Vöcking, B. (ed.) SAGT 2013. LNCS, vol. 8146, pp. 122–133. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  19. Monderer, D., Shapley, L.: Potential games. Games and economic behavior 14(1), 124–143 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  20. Nisan, N., Roughgarden, T., Tardos, É., Vazirani, V.V.: Algorithmic game theory, chapter 7. Cambridge University Press (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Blavatnik School of Computer Science, Tel Aviv University, Tel Aviv, Israel

    Michal Feldman & Ophir Friedler

Authors
  1. Michal Feldman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ophir Friedler
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ophir Friedler .

Editor information

Editors and Affiliations

  1. Reykjavik University, Reykjavik, Iceland

    Magnús M. Halldórsson

  2. Kyoto University, Kyoto, Japan

    Kazuo Iwama

  3. The University of Tokyo, Tokyo, Japan

    Naoki Kobayashi

  4. Technische Universiteit Eindhoven, Eindhoven, The Netherlands

    Bettina Speckmann

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Feldman, M., Friedler, O. (2015). A Unified Framework for Strong Price of Anarchy in Clustering Games. In: Halldórsson, M., Iwama, K., Kobayashi, N., Speckmann, B. (eds) Automata, Languages, and Programming. ICALP 2015. Lecture Notes in Computer Science(), vol 9135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47666-6_48

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-47666-6_48

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-47665-9

  • Online ISBN: 978-3-662-47666-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation