A Momentum-Based Approach to Learning Nash Equilibria

  • Huaxiang Zhang
  • Peide Liu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4088)


Learning a Nash equilibrium of a game is challengeable, and the issue of learning all the Nash equilibria seems intractable. This paper investigates the effectiveness of a momentum-based approach to learning the Nash equilibria of a game. Experimental results show the proposed algorithm can learn a Nash equilibrium in each learning iteration for a normal form strategic game. By employing a deflection technique, it can learn almost all the existing Nash equilibria of a game.


Nash Equilibrium Pure Strategy Stochastic Game Strategic Game Matrix 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.


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  1. 1.
    Vrieze, O.J., Tij, S.H.: Fictitious play applied to sequence of games and discounted stochastic games. International Journal of Game Theory 11(2), 71–85 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Claus, C., Boutilier, C.: The dynamics of reinforcement learning in cooperative multiagent systems. In: proceedings of 15th National Conference on Artificial Intelligence (1998)Google Scholar
  3. 3.
    Verbeeck, K., Nowe, A., Lenaerts, T., Parent, J.: Learning to reach the pareto optimal Nash Equilibrium as a Team. In: McKay, B., Slaney, J.K. (eds.) Canadian AI 2002. LNCS (LNAI), vol. 2557, Springer, Heidelberg (2002)CrossRefGoogle Scholar
  4. 4.
    Littman, M.L.: Markov games as a framework for multiagent reinforcement learning. In: Proc: 11th international conference on machine learning, New Brunswick, NJ, pp. 157–163. Morgan Kaufmann, San Mateo (1994)Google Scholar
  5. 5.
    Hu, J., Wellman, M.P.: Nash Q-Learning for General-Sum Stochastic Games. Journal of Machine Learning research 1, 1–30 (2003)Google Scholar
  6. 6.
    Bowling, M., Veloso, M.: Multiagent learning using a variable learning rate. Artificial Intelligence 136, 215–250 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Singh, S., Kearns, M., Mansouv, Y.: Nash convergence of gradient dynamics in general-sum games. In: proceedings of the 17th conference on uncertainty in artificial intelligence, pp. 541–548 (2000)Google Scholar
  8. 8.
    Zhang, H., Huang, S.: Convergent Gradient Ascent with Momentum in General-Sum Games. Neurocomputing 61, 445–449 (2004)CrossRefGoogle Scholar
  9. 9.
    Mckevey, R.D.: A Liapunov function for Nash equilibria. Technical Report, California institute of Technical Report, California Institute of Technology (1991)Google Scholar
  10. 10.
    Mckelvey, R.D., Mclennan, A., Turocy, T.: Gambit Command language, California Institute of Technology (2000)Google Scholar
  11. 11.
    Hansan, N., Stermer, A.: Completely derandomized self-adaption in evolution strategies. Evolutionary Computation 9(2), 159–195 (2001)CrossRefGoogle Scholar
  12. 12.
    Kennedy, J., Eberhart, R.C.: Swarm intelligence. Morgan Kaufmann Publishers, Los Altos (2001)Google Scholar
  13. 13.
    Pavlids, N.G., Parsopoulos, K.E., Vrahatis, M.N.: Computing Nash equilibria through computational intelligence methods 175, 113–136 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Huaxiang Zhang
    • 1
  • Peide Liu
    • 2
  1. 1.Dept. of Computer ScienceShandong Normal UniversityJinanChina
  2. 2.Dept. of Computer ScienceShandong Economics UniversityJinanChina

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