IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/1089.html
   My bibliography  Save this paper

On the Number of Nash Equilibria in a Bimatrix Game

Author

Abstract

We show that if y is an odd integer between 1 and 2^{n} - 1, there is an n x n bimatrix game with exactly y Nash equilibria (NE). We conjecture that this 2^{n} - 1 is a tight upper for n

Suggested Citation

  • Thomas Quint & Martin Shubik, 1994. "On the Number of Nash Equilibria in a Bimatrix Game," Cowles Foundation Discussion Papers 1089, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1089
    Note: CFP 958.
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d10/d1089.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Quint, Thomas & Shubik, Martin, 2002. "A bound on the number of Nash equilibria in a coordination game," Economics Letters, Elsevier, vol. 77(3), pages 323-327, November.
    2. Barany, I & Lee, J & Shubik, M, 1992. "Classification of Two-Person Ordinal Bimatrix Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(3), pages 267-290.
    3. B. Curtis Eaves, 1971. "The Linear Complementarity Problem," Management Science, INFORMS, vol. 17(9), pages 612-634, May.
    4. Powers, Imelda Yeung, 1990. "Limiting Distributions of the Number of Pure Strategy Nash Equilibria in N-Person Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(3), pages 277-286.
    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. Bade, Sophie & Haeringer, Guillaume & Renou, Ludovic, 2007. "More strategies, more Nash equilibria," Journal of Economic Theory, Elsevier, vol. 135(1), pages 551-557, July.
    2. Keiding, Hans, 1997. "On the Maximal Number of Nash Equilibria in ann x nBimatrix Game," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 148-160, October.
    3. Quint, Thomas & Shubik, Martin, 2002. "A bound on the number of Nash equilibria in a coordination game," Economics Letters, Elsevier, vol. 77(3), pages 323-327, November.
    4. McLennan, Andrew, 1997. "The Maximal Generic Number of Pure Nash Equilibria," Journal of Economic Theory, Elsevier, vol. 72(2), pages 408-410, February.
    5. Thomas Quint & Martin Shubik & Dickey Yan, 1995. "Dumb Bugs and Bright Noncooperative Players: Games, Context and Behavior," Cowles Foundation Discussion Papers 1094, Cowles Foundation for Research in Economics, Yale University.

    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. Stanford, William, 2004. "Individually rational pure strategies in large games," Games and Economic Behavior, Elsevier, vol. 47(1), pages 221-233, April.
    2. Tom Johnston & Michael Savery & Alex Scott & Bassel Tarbush, 2023. "Game Connectivity and Adaptive Dynamics," Papers 2309.10609, arXiv.org, revised Oct 2024.
    3. Heinrich, Torsten & Wiese, Samuel, 2020. "The Frequency of Convergent Games under Best-Response Dynamics," INET Oxford Working Papers 2020-24, Institute for New Economic Thinking at the Oxford Martin School, University of Oxford.
    4. Michael R. Powers & Martin Shubik & Wen Wang, 2016. "Expected Worth for 2 � 2 Matrix Games with Variable Grid Sizes," Cowles Foundation Discussion Papers 2039, Cowles Foundation for Research in Economics, Yale University.
    5. Fabrizio Germano, 2006. "On some geometry and equivalence classes of normal form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(4), pages 561-581, November.
    6. S. Mishra & T. K. Kumar, 1997. "On the Probability of Existence of Pure Equilibria in Matrix Games," Journal of Optimization Theory and Applications, Springer, vol. 94(3), pages 765-770, September.
    7. Torsten Heinrich & Yoojin Jang & Luca Mungo & Marco Pangallo & Alex Scott & Bassel Tarbush & Samuel Wiese, 2021. "Best-response dynamics, playing sequences, and convergence to equilibrium in random games," Papers 2101.04222, arXiv.org, revised Nov 2022.
    8. Richárd Kicsiny & Zoltán Varga, 2023. "New algorithm for checking Pareto optimality in bimatrix games," Annals of Operations Research, Springer, vol. 320(1), pages 235-259, January.
    9. Ben Amiet & Andrea Collevecchio & Marco Scarsini & Ziwen Zhong, 2021. "Pure Nash Equilibria and Best-Response Dynamics in Random Games," Mathematics of Operations Research, INFORMS, vol. 46(4), pages 1552-1572, November.
    10. McLennan, Andrew & Park, In-Uck, 1999. "Generic 4 x 4 Two Person Games Have at Most 15 Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 26(1), pages 111-130, January.
    11. S. R. Mohan, 1997. "Degeneracy Subgraph of the Lemke Complementary Pivot Algorithm and Anticycling Rule," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 409-423, August.
    12. Rinott, Yosef & Scarsini, Marco, 2000. "On the Number of Pure Strategy Nash Equilibria in Random Games," Games and Economic Behavior, Elsevier, vol. 33(2), pages 274-293, November.
    13. Thiruvankatachari Parthasarathy & Gomatam Ravindran & Sunil Kumar, 2022. "On Semimonotone Matrices, $$R_0$$ R 0 -Matrices and Q-Matrices," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 131-147, October.
    14. Stanford, William, 1999. "On the number of pure strategy Nash equilibria in finite common payoffs games," Economics Letters, Elsevier, vol. 62(1), pages 29-34, January.
    15. Y. B. Zhao & J. Y. Han & H. D. Qi, 1999. "Exceptional Families and Existence Theorems for Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 101(2), pages 475-495, May.
    16. Thomas Quint & Martin Shubik & Dickey Yan, 1995. "Dumb Bugs and Bright Noncooperative Players: Games, Context and Behavior," Cowles Foundation Discussion Papers 1094, Cowles Foundation for Research in Economics, Yale University.
    17. Pangallo, Marco & Heinrich, Torsten & Jang, Yoojin & Scott, Alex & Tarbush, Bassel & Wiese, Samuel & Mungo, Luca, 2021. "Best-Response Dynamics, Playing Sequences, And Convergence To Equilibrium In Random Games," INET Oxford Working Papers 2021-23, Institute for New Economic Thinking at the Oxford Martin School, University of Oxford.
    18. Samuel C. Wiese & Torsten Heinrich, 2022. "The Frequency of Convergent Games under Best-Response Dynamics," Dynamic Games and Applications, Springer, vol. 12(2), pages 689-700, June.
    19. Hwang, Sung-Ha & Rey-Bellet, Luc, 2020. "Strategic decompositions of normal form games: Zero-sum games and potential games," Games and Economic Behavior, Elsevier, vol. 122(C), pages 370-390.
    20. Herings, P. Jean-Jacques & van den Elzen, Antoon, 2002. "Computation of the Nash Equilibrium Selected by the Tracing Procedure in N-Person Games," Games and Economic Behavior, Elsevier, vol. 38(1), pages 89-117, January.

    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:cwl:cwldpp:1089. 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: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.html .

    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.