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Finding all Nash equilibria of a finite game using polynomial algebra

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  • Ruchira Datta

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Abstract

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Suggested Citation

  • Ruchira Datta, 2010. "Finding all Nash equilibria of a finite game using polynomial algebra," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 55-96, January.
  • Handle: RePEc:spr:joecth:v:42:y:2010:i:1:p:55-96
    DOI: 10.1007/s00199-009-0447-z
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    References listed on IDEAS

    as
    1. 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.
    2. McLennan, A., 1999. "The Expected Number for Real Roots of a Multihomogeneous System of Polynominal Equations," Papers 307, Minnesota - Center for Economic Research.
    3. McKelvey, Richard D. & McLennan, Andrew, 1997. "The Maximal Number of Regular Totally Mixed Nash Equilibria," Journal of Economic Theory, Elsevier, vol. 72(2), pages 411-425, February.
    4. P. Herings & Ronald Peeters, 2005. "A Globally Convergent Algorithm to Compute All Nash Equilibria for n-Person Games," Annals of Operations Research, Springer, vol. 137(1), pages 349-368, July.
    5. P.J.J. Herings & R. Peeters, 2001. "A Globally Convergent Algorithm to Compute Stationary Equilibria in Stochastic Games," Game Theory and Information 0205001, EconWPA.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Tao Zha & Juan F. Rubio-Ramirez & Daniel F. Waggoner & Andrew T. Foerster, 2010. "Perturbation Methods for Markov-Switching Models," 2010 Meeting Papers 239, Society for Economic Dynamics.
    2. 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.
    3. Andrew Foerster & Juan F. Rubio‐Ramírez & Daniel F. Waggoner & Tao Zha, 2016. "Perturbation methods for Markov‐switching dynamic stochastic general equilibrium models," Quantitative Economics, Econometric Society, vol. 7(2), pages 637-669, July.
    4. 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.
    5. Iryna Topolyan, 2013. "Existence of perfect equilibria: a direct proof," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(3), pages 697-705, August.
    6. repec:bpj:bejtec:v:18:y:2018:i:1:p:15:n:14 is not listed on IDEAS
    7. repec:spr:annopr:v:254:y:2017:i:1:d:10.1007_s10479-017-2453-z is not listed on IDEAS
    8. Li, Xiaoliang & Wang, Dongming, 2014. "Computing equilibria of semi-algebraic economies using triangular decomposition and real solution classification," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 48-58.

    More about this item

    Keywords

    Nash equilibrium; Normal form game; Algebraic variety; C72;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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