IDEAS home Printed from https://ideas.repec.org/p/ecl/stabus/1984.html
   My bibliography  Save this paper

Computing Equilibria of N-Player Games with Arbitrary Accuracy

Author

Listed:
  • Govindand, Srihari

    (U of Iowa)

  • Wilson, Robert B.

    (Stanford U)

Abstract

From a variant of Kuhn's triangulation we derive a discrete version of the Global Newton Method that yields an epsilon-equilibrium of an N-player game and then sequentially reduces epsilon toward zero to obtain any desired precision or the best precision for any number of iterations.

Suggested Citation

  • Govindand, Srihari & Wilson, Robert B., 2008. "Computing Equilibria of N-Player Games with Arbitrary Accuracy," Research Papers 1984, Stanford University, Graduate School of Business.
    • Handle: RePEc:ecl:stabus:1984
    as

    Download full text from publisher

    File URL: http://gsbapps.stanford.edu/researchpapers/library/RP1984.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Govindan, Srihari & Wilson, Robert, 2004. "Computing Nash equilibria by iterated polymatrix approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1229-1241, April.
    2. Srihari Govindan & Robert Wilson, 2010. "A decomposition algorithm for N-player games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 97-117, January.
    3. Talman, A.J.J. & van der Laan, G., 1980. "A new subdivision for computing fixed points with a homotopy algorithm," Other publications TiSEM d702630e-5e0d-4c31-bd1e-1, Tilburg University, School of Economics and Management.
    4. Govindan, Srihari & Wilson, Robert, 2003. "A global Newton method to compute Nash equilibria," Journal of Economic Theory, Elsevier, vol. 110(1), pages 65-86, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yiyin Cao & Chuangyin Dang & Yabin Sun, 2022. "Complementarity Enhanced Nash’s Mappings and Differentiable Homotopy Methods to Select Perfect Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 533-563, February.
    2. P. Giovani Palafox-Alcantar & Dexter V. L. Hunt & Chris D. F. Rogers, 2020. "A Hybrid Methodology to Study Stakeholder Cooperation in Circular Economy Waste Management of Cities," Energies, MDPI, vol. 13(7), pages 1-30, April.
    3. Sam Ganzfried, 2020. "Fast Complete Algorithm for Multiplayer Nash Equilibrium," Papers 2002.04734, arXiv.org, revised Jan 2023.
    4. Dang, Chuangyin & Meng, Xiaoxuan & Talman, Dolf, 2015. "An Interior-Point Path-Following Method for Computing a Perfect Stationary Point of a Polynomial Mapping on a Polytope," Discussion Paper 2015-019, Tilburg University, Center for Economic Research.
    5. P. Herings & Ronald Peeters, 2010. "Homotopy methods to compute equilibria in game theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 119-156, January.
    6. Bernhard Stengel, 2010. "Computation of Nash equilibria in finite games: introduction to the symposium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 1-7, January.
    7. Cao, Yiyin & Dang, Chuangyin & Xiao, Zhongdong, 2022. "A differentiable path-following method to compute subgame perfect equilibria in stationary strategies in robust stochastic games and its applications," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1032-1050.
    8. Turocy, Theodore L., 2005. "A dynamic homotopy interpretation of the logistic quantal response equilibrium correspondence," Games and Economic Behavior, Elsevier, vol. 51(2), pages 243-263, May.
    9. Dang, Chuangyin & Meng, Xiaoxuan & Talman, Dolf, 2015. "An Interior-Point Path-Following Method for Computing a Perfect Stationary Point of a Polynomial Mapping on a Polytope," Discussion Paper 2015-019, Tilburg University, Center for Economic Research.
    10. Theodore L. Turocy, 2002. "A Dynamic Homotopy Interpretation of Quantal Response Equilibrium Correspondences," Game Theory and Information 0212001, University Library of Munich, Germany, revised 16 Oct 2003.
    11. Srihari Govindan & Robert Wilson, 2010. "A decomposition algorithm for N-player games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 97-117, January.
    12. Doraszelski, Ulrich & Satterthwaite, Mark, 2007. "Computable Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity," CEPR Discussion Papers 6212, C.E.P.R. Discussion Papers.
    13. Ulrich Doraszelski & Mark Satterthwaite, 2007. "Computable Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity," Levine's Bibliography 321307000000000912, UCLA Department of Economics.
    14. Jiang, Albert Xin & Leyton-Brown, Kevin & Bhat, Navin A.R., 2011. "Action-Graph Games," Games and Economic Behavior, Elsevier, vol. 71(1), pages 141-173, January.
    15. Yiyin Cao & Yin Chen & Chuangyin Dang, 2024. "A Differentiable Path-Following Method with a Compact Formulation to Compute Proper Equilibria," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 377-396, March.
    16. Cao, Yiyin & Dang, Chuangyin, 2022. "A variant of Harsanyi's tracing procedures to select a perfect equilibrium in normal form games," Games and Economic Behavior, Elsevier, vol. 134(C), pages 127-150.
    17. Porter, Ryan & Nudelman, Eugene & Shoham, Yoav, 2008. "Simple search methods for finding a Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 63(2), pages 642-662, July.
    18. Govindan, Srihari & Wilson, Robert, 2009. "Global Newton Method for stochastic games," Journal of Economic Theory, Elsevier, vol. 144(1), pages 414-421, January.
    19. Doup, T.M. & Talman, A.J.J., 1985. "A continuous deformation algorithm on the product space of unit simplices," Research Memorandum FEW 168, Tilburg University, School of Economics and Management.
    20. Doup, T.M. & Talman, A.J.J., 1986. "A continuous deformation algorithm on the product space of unit simplices (Revised version)," Other publications TiSEM e05eb62e-3cc0-48d7-8880-6, Tilburg University, School of Economics and Management.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ecl:stabus:1984. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/gsstaus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.