Skip to main content
SpringerLink
Log in

Profitable Deviation Strong Equilibria

  • Conference paper
  • First Online:
Algorithmic Decision Theory (ADT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9346))

Included in the following conference series:

  • 1344 Accesses

Abstract

This paper deals with states that are immune to group deviations. Group deviations help the players of a strategic game to escape from undesirable states but they compromise the stability of a system. We propose and analyse a solution concept, called profitable deviation strong equilibrium, which is between two well-known equilibria: the strong equilibrium and the super strong equilibrium. The former precludes joint deviations by groups of players who all benefit. The latter is more demanding in the sense that at least one member of a deviating coalition must be better off while the other members cannot be worst off. We study the existence, computation and convergence to a profitable deviation strong equilibrium in three important games in algorithmic game theory: job scheduling, max cut and singleton congestion game.

Supported by the project ANR-14-CE24-0007-01 CoCoRICo-CoDec.

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

Notes

  1. 1.

    Also known as strictly strong Nash equilibrium [28].

  2. 2.

    Note that the max cut game can be defined as a congestion game, but not as a singleton congestion game, so the results of Sect. 5 do not apply.

References

  1. Andelman, N., Feldman, M., Mansour, Y.: Strong price of anarchy. Games Econ. Behav. 65(2), 289–317 (2009)

    Article  MathSciNet  Google Scholar 

  2. Anshelevich, E., Caskurlu, B., Hate, A.: Partition equilibrium always exists in resource selection games. Theory Comput. Syst. 53(1), 73–85 (2013)

    Article  MathSciNet  Google Scholar 

  3. Anshelevich, E., Postl, J., Wexler, T.: Assignment games with conflicts: price of total anarchy and convergence results via semi-smoothness. CoRR abs/1304.5149 (2013). http://arxiv.org/abs/1304.5149

  4. Aumann, R.J.: Acceptable points in general cooperative n-person games. In: Tucker, A.W., Luce, R.D. (eds.) Contribution to the Theory of Games. Annals of Mathematics Studies, 40, vol. IV, pp. 287–324. Princeton University Press (1959)

    Google Scholar 

  5. Caragiannis, I., Fanelli, A., Gravin, N.: Short sequences of improvement moves lead to approximate equilibria in constraint satisfaction games. In: Lavi, R. (ed.) SAGT 2014. LNCS, vol. 8768, pp. 49–60. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  6. Chen, P., de Keijzer, B., Kempe, D., Schäfer, G.: Altruism and its impact on the price of anarchy. ACM Trans. Econ. Comput. 2(4), 17 (2014). http://doi.acm.org/10.1145/2597893

    Article  Google Scholar 

  7. Chien, S., Sinclair, A.: Strong and pareto price of anarchy in congestion games. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009, Part I. LNCS, vol. 5555, pp. 279–291. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  8. Epstein, L., Kleiman, E.: On the quality and complexity of Pareto equilibria in the job scheduling game. In: Sonenberg, L., Stone, P., Tumer, K., Yolum, P. (eds.) 10th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2011). IFAAMAS, Taipei, Taiwan, 2–6 May 2011, vol. 1–3, pp. 525–532 (2011). http://portal.acm.org/citation.cfm?id=2031692&CFID=54178199&CFTOKEN=61392764

  9. Epstein, L., Kleiman, E., van Stee, R.: Maximizing the minimum load: the cost of selfishness. In: Leonardi, S. (ed.), [21], pp. 232–243 (2009)

    Google Scholar 

  10. Epstein, L., van Stee, R.: Maximizing the minimum load for selfish agents. Theor. Comput. Sci. 411(1), 44–57 (2010)

    Article  MathSciNet  Google Scholar 

  11. Even-Dar, E., Kesselman, A., Mansour, Y.: Convergence time to Nash equilibrium in load balancing. ACM Trans. Algorithms 3(3) (2007)

    Google Scholar 

  12. Feldman, M., Tennenholtz, M.: Partition equilibrium. In: Mavronicolas, M., Papadopoulou, V.G. (eds.) SAGT 2009. LNCS, vol. 5814, pp. 48–59. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  13. Fotakis, D.A., Kontogiannis, S.C., Koutsoupias, E., Mavronicolas, M., Spirakis, P.G.: The structure and complexity of Nash equilibria for a selfish routing game. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, p. 123. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  14. 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 

  15. 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 

  16. Gourvès, L., Monnot, J., Moretti, S., Thang, N.: Congestion games with capacitated resources. Theory of Computing Systems pp. 1–19 (2014)

    Google Scholar 

  17. Hoefer, M.: Cost Sharing and Clustering under Distributed Competition. Ph.D. thesis, Universität Konstanz (2007)

    Google Scholar 

  18. Hoefer, M., Penn, M., Polukarov, M., Skopalik, A., Vöcking, B.: Considerate equilibrium. In: Walsh, T. (ed.) IJCAI. pp. 234–239. IJCAI/AAAI (2011)

    Google Scholar 

  19. Hoefer, M., Skopalik, A.: On the complexity of Pareto-optimal Nash and strong equilibria. Theory Comput. Syst. 53(3), 441–453 (2013). doi:10.1007/s00224-012-9433-0

    Article  MathSciNet  MATH  Google Scholar 

  20. Holzman, R., Law-Yone, N.: Strong equilibrium in congestion games. Games and Economic Behavior 21(1–2), 85–101 (1997)

    Article  MathSciNet  Google Scholar 

  21. Leonardi, S. (ed.): Internet and Network Economics, 5th International Workshop, WINE 2009, Rome, Italy, December 14–18, 2009. Proceedings, Lecture Notes in Computer Science, vol. 5929. Springer (2009)

    Google Scholar 

  22. Milchtaich, I.: Congestion games with player-specific payoff functions. Games and Economic Behavior 13(1), 111–124 (1996), http://www.sciencedirect.com/science/article/pii/S0899825696900275

  23. Monderer, D., Shapley, L.S.: Potential games. Games and Economic Behavior 14(1), 124–143 (1996), http://www.sciencedirect.com/science/article/pii/S0899825696900445

  24. Nash, J.: Non-cooperative Games. The Annals of Mathematics 54(2), 286–295 (1951)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  26. Rozenfeld, O., Tennenholtz, M.: Strong and Correlated Strong Equilibria in Monotone Congestion Games. In: Spirakis, P.G., Mavronicolas, M., Kontogiannis, S.C. (eds.) WINE 2006. LNCS, vol. 4286, pp. 74–86. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  27. Schäffer, A.A., Yannakakis, M.: Simple local search problems that are hard to solve. SIAM J. Comput. 20(1), 56–87 (1991). doi:10.1137/0220004

    Article  MathSciNet  MATH  Google Scholar 

  28. Voorneveld, M.: Potential Games and Interactive Decisions with Multiple Criteria. Ph.D. thesis, Tilburg University (1999)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CNRS UMR 7243, Université Paris Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris Cedex 16, France

    Laurent Gourvès

Authors
  1. Laurent Gourvès
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Laurent Gourvès .

Editor information

Editors and Affiliations

  1. University of New South Wales, Kensington, Australia

    Toby Walsh

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Gourvès, L. (2015). Profitable Deviation Strong Equilibria. In: Walsh, T. (eds) Algorithmic Decision Theory. ADT 2015. Lecture Notes in Computer Science(), vol 9346. Springer, Cham. https://doi.org/10.1007/978-3-319-23114-3_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-23114-3_15

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23113-6

  • Online ISBN: 978-3-319-23114-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation