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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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  • 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

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    1. McLennan, A., 1999. "The Expected Number for Real Roots of a Multihomogeneous System of Polynominal Equations," Papers 307, Minnesota - Center for Economic Research.
    2. 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.
    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.J.J. Herings & R. Peeters, 2001. "A Globally Convergent Algorithm to Compute Stationary Equilibria in Stochastic Games," Game Theory and Information 0205001, University Library of Munich, Germany.
    5. 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.
    6. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    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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    Cited by:

    1. Kocięcki, Andrzej & Kolasa, Marcin, 2023. "A solution to the global identification problem in DSGE models," Journal of Econometrics, Elsevier, vol. 236(2).
    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. 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.
    4. Antônio Francisco Neto & Carolina Rodrigues Fonseca, 2019. "An approach via generating functions to compute power indices of multiple weighted voting games with incompatible players," Annals of Operations Research, Springer, vol. 279(1), pages 221-249, August.
    5. Felix Kubler & Karl Schmedders, 2010. "Tackling Multiplicity of Equilibria with Gröbner Bases," Operations Research, INFORMS, vol. 58(4-part-2), pages 1037-1050, August.
    6. 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.
    7. Fedor Iskhakov & John Rust & Bertel Schjerning, 2016. "Recursive Lexicographical Search: Finding All Markov Perfect Equilibria of Finite State Directional Dynamic Games," Review of Economic Studies, Oxford University Press, vol. 83(2), pages 658-703.
    8. Ivonne Callejas & Srihari Govindan & Lucas Pahl, 2021. "A Finite Characterization of Perfect Equilibria," Papers 2111.01638, arXiv.org.
    9. 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.
    10. 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.
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    12. David Pozo & Enzo Sauma & Javier Contreras, 2017. "Basic theoretical foundations and insights on bilevel models and their applications to power systems," Annals of Operations Research, Springer, vol. 254(1), pages 303-334, July.

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    More about this item

    Keywords

    Nash equilibrium; Normal form game; Algebraic variety; C72;
    All these keywords.

    JEL classification:

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

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