IDEAS home Printed from https://ideas.repec.org/a/ecm/emetrp/v70y2002i2p693-715.html
   My bibliography  Save this article

Computing Normal Form Perfect Equilibria for Extensive Two-Person Games

Author

Listed:
  • Bernhard von Stengel

    () (Department of Mathematics, London School of Economics, Houghton St, London WC2A 2AE, United Kingdom)

  • Antoon van den Elzen

    () (Div. of Humanities and Social Sciences 227-88, California Institute of Technology, Pasadena, CA 91125, U.S.A.)

  • Dolf Talman

    () (Div. of Humanities and Social Sciences 227-88, California Institute of Technology, Pasadena, CA 91125, U.S.A.)

Abstract

This paper presents an algorithm for computing an equilibrium of an extensive two-person game with perfect recall. The method is computationally efficient by virtue of using the sequence form, whose size is proportional to the size of the game tree. The equilibrium is traced on a piecewise linear path in the sequence form strategy space from an arbitrary starting vector. If the starting vector represents a pair of completely mixed strategies, then the equilibrium is normal form perfect. Computational experiments compare the sequence form and the reduced normal form, and show that only the sequence form is tractable for larger games. Copyright The Econometric Society 2002.

Suggested Citation

  • Bernhard von Stengel & Antoon van den Elzen & Dolf Talman, 2002. "Computing Normal Form Perfect Equilibria for Extensive Two-Person Games," Econometrica, Econometric Society, vol. 70(2), pages 693-715, March.
  • Handle: RePEc:ecm:emetrp:v:70:y:2002:i:2:p:693-715
    as

    Download full text from publisher

    File URL: http://www.blackwellpublishing.com/ecta/asp/abstract.asp?iid=2&aid=300&vid=70
    File Function: link to full text
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Wilson, Robert, 1992. "Computing Simply Stable Equilibria," Econometrica, Econometric Society, vol. 60(5), pages 1039-1070, September.
    2. Selten, Reinhard, 1988. "Evolutionary stability in extensive two-person games - correction and further development," Mathematical Social Sciences, Elsevier, vol. 16(3), pages 223-266, December.
    3. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, January.
    4. Bernhard von Stengel & Antoon van den Elzen & Dolf Talman, 2002. "Computing Normal Form Perfect Equilibria for Extensive Two-Person Games," Econometrica, Econometric Society, vol. 70(2), pages 693-715, March.
    5. Koller, Daphne & Megiddo, Nimrod, 1996. "Finding Mixed Strategies with Small Supports in Extensive Form Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(1), pages 73-92.
    6. Robert Wilson, 1972. "Computing Equilibria of Two-Person Games from the Extensive Form," Management Science, INFORMS, vol. 18(7), pages 448-460, March.
    7. Dai, Y. & Talman, A.J.J., 1990. "Linear stationary point problems on unbounded polyhedra," Discussion Paper 1990-67, Tilburg University, Center for Economic Research.
    8. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    9. Von Stengel, Bernhard, 2002. "Computing equilibria for two-person games," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 45, pages 1723-1759 Elsevier.
    10. Talman, A.J.J. & van den Elzen, A.H., 1991. "A procedure for finding Nash equilibria in bi-matrix games," Other publications TiSEM 14df3398-1521-43ad-8803-a, Tilburg University, School of Economics and Management.
    11. Gilboa, Itzhak & Zemel, Eitan, 1989. "Nash and correlated equilibria: Some complexity considerations," Games and Economic Behavior, Elsevier, vol. 1(1), pages 80-93, March.
    12. Talman, A.J.J. & Dai, Y., 1993. "Linear stationary point problems on unbounded polyhedra," Other publications TiSEM 17e8253b-bf0f-4b64-82fb-7, Tilburg University, School of Economics and Management.
    13. von Stengel, Bernhard, 1996. "Efficient Computation of Behavior Strategies," Games and Economic Behavior, Elsevier, vol. 14(2), pages 220-246, June.
    14. Kamiya, K. & Talman, A.J.J., 1990. "Linear stationary point problems," Discussion Paper 1990-22, Tilburg University, Center for Economic Research.
    15. van den Elzen, Antoon & Talman, Dolf, 1999. "An Algorithmic Approach toward the Tracing Procedure for Bi-matrix Games," Games and Economic Behavior, Elsevier, vol. 28(1), pages 130-145, July.
    16. Koller, Daphne & Megiddo, Nimrod, 1992. "The complexity of two-person zero-sum games in extensive form," Games and Economic Behavior, Elsevier, vol. 4(4), pages 528-552, October.
    17. Koller, Daphne & Megiddo, Nimrod & von Stengel, Bernhard, 1996. "Efficient Computation of Equilibria for Extensive Two-Person Games," Games and Economic Behavior, Elsevier, vol. 14(2), pages 247-259, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rahul Savani & Bernhard Stengel, 2015. "Game Theory Explorer: software for the applied game theorist," Computational Management Science, Springer, vol. 12(1), pages 5-33, January.
    2. Bade, Sophie & Haeringer, Guillaume & Renou, Ludovic, 2007. "More strategies, more Nash equilibria," Journal of Economic Theory, Elsevier, vol. 135(1), pages 551-557, July.
    3. repec:eee:ejores:v:266:y:2018:i:2:p:622-638 is not listed on IDEAS
    4. Stuart McDonald & Liam Wagner, 2010. "The Computation of Perfect and Proper Equilibrium for Finite Games via Simulated Annealing," Risk & Uncertainty Working Papers WPR10_1, Risk and Sustainable Management Group, University of Queensland, revised Apr 2010.
    5. Bernhard von Stengel & Antoon van den Elzen & Dolf Talman, 2002. "Computing Normal Form Perfect Equilibria for Extensive Two-Person Games," Econometrica, Econometric Society, vol. 70(2), pages 693-715, March.
    6. Stuart McDonald & Liam Wagner, 2013. "A Stochastic Search Algorithm for the Computation of Perfect and Proper Equilibria," Discussion Papers Series 480, School of Economics, University of Queensland, Australia.
    7. Echenique, Federico, 2007. "Finding all equilibria in games of strategic complements," Journal of Economic Theory, Elsevier, vol. 135(1), pages 514-532, July.
    8. Conitzer, Vincent & Sandholm, Tuomas, 2008. "New complexity results about Nash equilibria," Games and Economic Behavior, Elsevier, vol. 63(2), pages 621-641, July.
    9. F. Forges & B. von Stengel, 2002. "Computionally Efficient Coordination in Games Trees," THEMA Working Papers 2002-05, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    10. Herings, P. Jean-Jacques & Peeters, Ronald J. A. P., 2004. "Stationary equilibria in stochastic games: structure, selection, and computation," Journal of Economic Theory, Elsevier, vol. 118(1), pages 32-60, September.
    11. Rahul Savani & Bernhard von Stengel, 2016. "Unit vector games," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(1), pages 7-27, March.
    12. Echenique, Federico, 2002. "Finding All Equilibria," Working Papers 1153, California Institute of Technology, Division of the Humanities and Social Sciences.
    13. Yukio KORIYAMA & Matias Nunez, 2014. "Hybrid Procedures," THEMA Working Papers 2014-02, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    14. repec:eee:reensy:v:93:y:2008:i:11:p:1740-1750 is not listed on IDEAS

    More about this item

    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:ecm:emetrp:v:70:y:2002:i:2:p:693-715. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum). General contact details of provider: http://edirc.repec.org/data/essssea.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.