A Game-Theoretic Memory Mechanism for Coevolution

  • Sevan G. Ficici
  • Jordan B. Pollack
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2723)


One problem associated with coevolutionary algorithms is that of forgetting, where one or more previously acquired traits are lost only to be needed later. We introduce a new coevolutionary memory mechanism to help prevent forgetting that is built upon game-theoretic principles, specifically Nash equilibrium. This “Nash memory” mechanism has the following properties: 1) It accumulates a collection of salient traits discovered by search, and represents this collection as a mixed strategy. 2) This mixed strategy monotonically approaches the quality of a Nash equilibrium strategy as search progresses, thus acting as a “ratchet” mechanism. 3) The memory naturally embodies the result (solution) obtained by the coevolutionary process. 4) The memory appropriately handles intransitive cycles (subject to resource limitations). We demonstrate our Nash memory using Watson and Pollack’s intransitive numbers game, and compare its performance to the conventional “Hall of Fame” memory and the more recently proposed Dominance Tournament.


Artificial Intelligence Data Processing Nash Equilibrium Resource Limitation Problem Complexity 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. Brooks and P. Maes, editors. Proc. 4th Conf. on Artif. Life. MIT Press, 1994.Google Scholar
  2. 2.
    D. Cliff and G. F. Miller. Tracking the red queen: Measurments of adaptive progress in co-evolutionary simulations. In F. Moran et al., editors, 3rd Euro. Conf. on Artificial Life, pages 200–218. Springer Verlag, 1995.Google Scholar
  3. 3.
    S. G. Ficici, O. Melnik, and J. B. Pollack. A game-theoretic investigation of selection methods used in evolutionary algorithms. In A. Zalzala et al., editors, Proc. of 2000 Congress on Evolutionary Computation, pages 880–887. IEEE Press, 2000.Google Scholar
  4. 4.
    S. G. Ficici and J. B. Pollack. Challenges in coevolutionary learning: Arms-race dynamics, open-endedness, and mediocre stable states. In C. Adami et al., editors, Proc. of the Sixth Conf. on Artificial Life, pages 238–247. MIT Press, 1998.Google Scholar
  5. 5.
    D. Fudenberg and J. Tirole. Game Theory. MIT Press, 1998.Google Scholar
  6. 6.
    D. Goldberg. Genetic Algorithms in Search, Optimization, and Machine Learning. Addison Wesley, 1989.Google Scholar
  7. 7.
    S. Nolfi and D. Floreano. Co-evolving predator and prey robots: Do ‘arm races’ arise in artificial evolution? Artificial Life, 4(4):311–335, 1998.CrossRefGoogle Scholar
  8. 8.
    C. W. Reynolds. Competition, coevolution and the game of tag. In P. Maes, editors. Proc. 4th Conf. on Artif. Life. MIT Press, 1994 Brooks and Maes [1], pages 59–69.Google Scholar
  9. 9.
    C. Rosin and R. Belew. New methods for competitive co-evolution. Evolutionary Computation, 5(1):1–29, 1997.CrossRefGoogle Scholar
  10. 10.
    K. Sims. Evolving 3d morphology and behavior by competition. In P. Maes, editors. Proc. 4th Conf. on Artif. Life. MIT Press, 1994 Brooks and Maes [1], pages 28–39.Google Scholar
  11. 11.
    K. O. Stanley and R. Miikkulainen. The dominance tournament method of monitoring progress in coevolution. In A. Barry, editor, 2002 Genetic and Evolutionary Computation Conference Workshop Program, pages 242–248, 2002.Google Scholar
  12. 12.
    P. R. Thie. An Introduction to Linear Programming and Game Theory. John Wiley and Sons, 1988.Google Scholar
  13. 13.
    R. A. Watson and J. B. Pollack. Coevolutionary dynamics in a minimal substrate. In L. Spector et al., editors, Proc. 2001 Genetic and Evolutionary Computation Conf., pages 702–709. Morgan Kaufmann, 2001.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Sevan G. Ficici
    • 1
  • Jordan B. Pollack
    • 1
  1. 1.Department of Computer ScienceBrandeis UniversityWalthamUSA

Personalised recommendations