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Profitable Deviation Strong Equilibria

  • Laurent GourvèsEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9346)

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.

Keywords

Algorithmic game theory Equilibrium Group deviation 

References

  1. 1.
    Andelman, N., Feldman, M., Mansour, Y.: Strong price of anarchy. Games Econ. Behav. 65(2), 289–317 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Anshelevich, E., Caskurlu, B., Hate, A.: Partition equilibrium always exists in resource selection games. Theory Comput. Syst. 53(1), 73–85 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 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. 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. 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) Google Scholar
  6. 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 CrossRefzbMATHGoogle Scholar
  7. 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) CrossRefGoogle Scholar
  8. 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. 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. 10.
    Epstein, L., van Stee, R.: Maximizing the minimum load for selfish agents. Theor. Comput. Sci. 411(1), 44–57 (2010)CrossRefzbMATHGoogle Scholar
  11. 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. 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) CrossRefGoogle Scholar
  13. 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) CrossRefGoogle Scholar
  14. 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) CrossRefGoogle Scholar
  15. 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) CrossRefGoogle Scholar
  16. 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. 17.
    Hoefer, M.: Cost Sharing and Clustering under Distributed Competition. Ph.D. thesis, Universität Konstanz (2007)Google Scholar
  18. 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. 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 MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Holzman, R., Law-Yone, N.: Strong equilibrium in congestion games. Games and Economic Behavior 21(1–2), 85–101 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 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. 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. 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. 24.
    Nash, J.: Non-cooperative Games. The Annals of Mathematics 54(2), 286–295 (1951)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Rosenthal, R.W.: A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory 2, 65–67 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 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) CrossRefGoogle Scholar
  27. 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 MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Voorneveld, M.: Potential Games and Interactive Decisions with Multiple Criteria. Ph.D. thesis, Tilburg University (1999)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.CNRS UMR 7243Université Paris DauphineParis Cedex 16France

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