Potential Functions in Strategic Games

  • Paul G. Spirakis
  • Panagiota N. Panagopoulou
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7913)

Abstract

We investigate here several categories of strategic games and antagonistic situations that are known to admit potential functions, and are thus guaranteed to either possess pure Nash equilibria or to stabilize in some form of equilibrium in cases of stochastic potentials. Our goal is to indicate the generality of this method and to address its limits.

Keywords

Nash Equilibrium Pure Strategy Chromatic Number Congestion Game Strategic 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, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bilò, V., Fanelli, A., Flammini, M., Moscardelli, L.: Graphical Congestion Games. In: Papadimitriou, C., Zhang, S. (eds.) WINE 2008. LNCS, vol. 5385, pp. 70–81. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  2. 2.
    Chen, X., Xiaotie, D.: Settling the complexity of two-player Nash equilibrium. In: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2006), pp. 261–272 (2006)Google Scholar
  3. 3.
    Chien, S., Sinclair, A.: Convergence to approximate Nash equilibria in congestion games. In: Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2007), pp. 169–178 (2007)Google Scholar
  4. 4.
    Díaz, J., Goldberg, L.A., Mertzios, G.B., Richerby, D., Serna, M.J., Spirakis, P.G.: Approximating fixation probabilities in the generalized Moran process. In: Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2012), pp. 954–960 (2012)Google Scholar
  5. 5.
    Feige, U., Kilian, J.: Zero knowledge and the chromatic number. J. Comput. System Sci. 57(2), 187–199 (1998)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Fotakis, D., Gkatzelis, V., Kaporis, A.C., Spirakis, P.G.: The Impact of Social Ignorance on Weighted Congestion Games. In: Leonardi, S. (ed.) WINE 2009. LNCS, vol. 5929, pp. 316–327. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  7. 7.
    Fotakis, D., Kaporis, A.C., Spirakis, P.G.: Atomic congestion games: fast, myopic and concurrent. Theory Comput. Syst. 47(1), 38–59 (2010)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Fotakis, D., Kontogiannis, S., Spirakis, P.G.: Atomic congestion games among coalitions. ACM Transactions on Algorithms (TALG) 4(4), article No. 52 (2008)Google Scholar
  9. 9.
    Fotakis, D., Kontogiannis, S., Spirakis, P.G.: Selfish unsplittable flows. Theoretical Computer Science 348(2), 226–239 (2005)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Hajek, B.: Hitting-time and occupation-time bounds implied by drift analysis with applications. Advances in Applied Probability 14(3), 502–525 (1982)MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    He, J., Yao, X.: Drift analysis and average time complexity of evolutionary algorithms. Artificial Intelligence 127, 57–85 (2001)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Lieberman, E., Hauert, C., Nowak, M.A.: Evolutionary dynamics on graphs. Nature 433, 312–316 (2005)CrossRefGoogle Scholar
  13. 13.
    Monderer, D., Shapley, L.: Potential games. Games and Economic Behavior 14, 124–143 (1996)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Nash, J.F.: Non-cooperative games. Annals of Mathematics 54(2), 286–295 (1951)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Papadimitriou, C.H.: On the complexity of the parity argument and other inefficient proofs of existence. Journal of Computer and System Sciences 48(3), 498–532 (1994)MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Panagopoulou, P.N., Spirakis, P.G.: Algorithms for pure Nash equilibria in weighted congestion games. ACM Journal of Experimental Algorithmics 11 (2006)Google Scholar
  17. 17.
    Panagopoulou, P.N., Spirakis, P.G.: A game theoretic approach for efficient graph coloring. In: Hong, S.-H., Nagamochi, H., Fukunaga, T. (eds.) ISAAC 2008. LNCS, vol. 5369, pp. 183–195. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  18. 18.
    Panagopoulou, P.N., Spirakis, P.G.: Playing a game to bound the chromatic number. The American Mathematical Monthly 119(9), 771–778 (2012)MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    Rosenthal, R.W.: A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory 2, 65–67 (1973)MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Tarski, A.: A lattice-theoretical fixpoint theorem and its applications. Pacific Journals of Mathematics 5, 285–308 (1955)MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    Topkis, D.: Equilibrium points in nonzero-sum n-person submodular games. SIAM Journal of Control and Optimization 17, 773–787 (1979)MathSciNetMATHCrossRefGoogle Scholar
  22. 22.
    Uno, H.: Strategic complementarities and nested potential games. Journal of Mathematical Economics 47(6), 728–732 (2011)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Paul G. Spirakis
    • 1
    • 2
  • Panagiota N. Panagopoulou
    • 2
  1. 1.Computer Engineering and Informatics DepartmentUniversity of PatrasGreece
  2. 2.Computer Technology Institute & Press “Diophantus”Greece

Personalised recommendations