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On the Number of Nash Equilibria in a Bimatrix Game

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Author Info
Thomas Quint
Martin Shubik () (Cowles Foundation, Yale University, Cowles Foundation, Yale University)

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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 <= 3, and provide bounds on the number of NEs in m x n nondegenerate games when min(m,n) <= 4.

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File URL: http://cowles.econ.yale.edu/P/cd/d10b/d1089.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1089.

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Length: 17 pages
Date of creation: Dec 1994
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Publication status: Published in International Journal of Game Theory (1997), 26: 353-359
Handle: RePEc:cwl:cwldpp:1089

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Barany, I & Lee, J & Shubik, M, 1992. "Classification of Two-Person Ordinal Bimatrix Games," International Journal of Game Theory, Springer, vol. 21(3), pages 267-90.
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  2. Thomas Quint & Martin Shubik, 1995. "A Bound on the Number of Nash Equilibria in a Coordination Game," Cowles Foundation Discussion Papers 1095, Cowles Foundation, Yale University. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Thomas Quint & Martin Shubik & Dickey Yan, 1995. "Dumb Bugs and Bright Noncooperative Players: Games, Context and Behavior," Cowles Foundation Discussion Papers 1094, Cowles Foundation, Yale University. [Downloadable!]
  2. Thomas Quint & Martin Shubik, 1995. "A Bound on the Number of Nash Equilibria in a Coordination Game," Cowles Foundation Discussion Papers 1095, Cowles Foundation, Yale University. [Downloadable!]
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  3. Sophie Bade & Guillaume Haeringer & Ludovic Renou, 2005. "More strategies, more Nash equilibria," Game Theory and Information 0502001, EconWPA. [Downloadable!]
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