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Computing Equilibria of Two-Person Games from the Extensive Form

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  • Robert Wilson

    (Stanford University)

Abstract

The Lemke-Howson algorithm for computing equilibria of finite 2-person non-cooperative games in normal form is modified to restrict the computations to the ordinarily small portion corresponding to the strategies actually used by the players, and further it is shown that in games with perfect recall these strategies can be generated as needed from an auxiliary analysis of the players' decision trees derived from the extensive form of the game.

Suggested Citation

  • Robert Wilson, 1972. "Computing Equilibria of Two-Person Games from the Extensive Form," Management Science, INFORMS, vol. 18(7), pages 448-460, March.
    • Handle: RePEc:inm:ormnsc:v:18:y:1972:i:7:p:448-460
    DOI: 10.1287/mnsc.18.7.448
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Prakash Shenoy, 1998. "Game Trees For Decision Analysis," Theory and Decision, Springer, vol. 44(2), pages 149-171, April.
    5. Etessami, Kousha, 2021. "The complexity of computing a (quasi-)perfect equilibrium for an n-player extensive form game," Games and Economic Behavior, Elsevier, vol. 125(C), pages 107-140.
    6. 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.
    7. 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.

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