IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v42y2010i1p55-96.html
   My bibliography  Save this article

Finding all Nash equilibria of a finite game using polynomial algebra

Author

Listed:
  • Ruchira Datta

Abstract

No abstract is available for this item.

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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00199-009-0447-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00199-009-0447-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    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. 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.
    4. 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.
    5. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    6. 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.
    7. 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.
    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. Felix Kubler & Karl Schmedders, 2010. "Tackling Multiplicity of Equilibria with Gröbner Bases," Operations Research, INFORMS, vol. 58(4-part-2), pages 1037-1050, August.
    2. 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.
    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. Kocięcki, Andrzej & Kolasa, Marcin, 2023. "A solution to the global identification problem in DSGE models," Journal of Econometrics, Elsevier, vol. 236(2).
    5. 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.
    6. 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.
    7. Fedor Iskhakov & John Rust & Bertel Schjerning, 2016. "Recursive Lexicographical Search: Finding All Markov Perfect Equilibria of Finite State Directional Dynamic Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(2), pages 658-703.
    8. Whitmeyer Mark, 2018. "A Competitive Optimal Stopping Game," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 18(1), pages 1-15, January.
    9. Ivonne Callejas & Srihari Govindan & Lucas Pahl, 2021. "A Finite Characterization of Perfect Equilibria," Papers 2111.01638, arXiv.org.
    10. Andrew Foerster & Juan F. Rubio-Ramirez & Daniel F. Waggoner & Tao Zha, 2013. "Perturbation methods for Markov-switching DSGE models," FRB Atlanta Working Paper 2013-01, Federal Reserve Bank of Atlanta.
    11. 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.
    12. 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.
    13. 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.

    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. 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.
    2. 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.
    3. 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.
    4. Yang Zhan & Chuangyin Dang, 2021. "Computing equilibria for markets with constant returns production technologies," Annals of Operations Research, Springer, vol. 301(1), pages 269-284, June.
    5. 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.
    6. Battigalli, Pierpaolo & Bonanno, Giacomo, 1997. "The Logic of Belief Persistence," Economics and Philosophy, Cambridge University Press, vol. 13(1), pages 39-59, April.
    7. Szabó, György & Borsos, István & Szombati, Edit, 2019. "Games, graphs and Kirchhoff laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 416-423.
    8. Shi, Yi & Deng, Yawen & Wang, Guoan & Xu, Jiuping, 2020. "Stackelberg equilibrium-based eco-economic approach for sustainable development of kitchen waste disposal with subsidy policy: A case study from China," Energy, Elsevier, vol. 196(C).
    9. Marc Le Menestrel, 2003. "A one-shot Prisoners’ Dilemma with procedural utility," Economics Working Papers 819, Department of Economics and Business, Universitat Pompeu Fabra.
    10. Cheng‐Kuang Wu & Yi‐Ming Chen & Dachrahn Wu & Ching‐Lin Chi, 2020. "A Game Theory Approach for Assessment of Risk and Deployment of Police Patrols in Response to Criminal Activity in San Francisco," Risk Analysis, John Wiley & Sons, vol. 40(3), pages 534-549, March.
    11. Nasimeh Heydaribeni & Achilleas Anastasopoulos, 2019. "Linear Equilibria for Dynamic LQG Games with Asymmetric Information and Dependent Types," Papers 1909.04834, arXiv.org.
    12. Müller, Christoph, 2020. "Robust implementation in weakly perfect Bayesian strategies," Journal of Economic Theory, Elsevier, vol. 189(C).
    13. Hitoshi Matsushima, 2019. "Implementation without expected utility: ex-post verifiability," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(4), pages 575-585, December.
    14. Dasgupta Utteeyo, 2011. "Are Entry Threats Always Credible?," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 11(1), pages 1-41, December.
    15. Baran Han, 2018. "The role and welfare rationale of secondary sanctions: A theory and a case study of the US sanctions targeting Iran," Conflict Management and Peace Science, Peace Science Society (International), vol. 35(5), pages 474-502, September.
    16. Carlos Pimienta & Jianfei Shen, 2014. "On the equivalence between (quasi-)perfect and sequential equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 395-402, May.
    17. Asheim, Geir & Søvik, Ylva, 2003. "The semantics of preference-based belief operators," Memorandum 05/2003, Oslo University, Department of Economics.
    18. Salvador Barberà & Anke Gerber, 2024. "On the Endogenous Order of Play in Sequential Games," Working Papers 1443, Barcelona School of Economics.
    19. 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.
    20. Wang, Yafeng & Graham, Brett, 2009. "Generalized Maximum Entropy estimation of discrete sequential move games of perfect information," MPRA Paper 21331, University Library of Munich, Germany.

    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

    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:spr:joecth:v:42:y:2010:i:1:p:55-96. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.