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A Theorem on the Number of Nash Equilibria in a Bimatrix Game

Author

Listed:
  • Martin Shubik

    (Department of Economics, Yale University, P.O. Box 208281, New Haven, Connecticut 06520-8281, USA)

  • Thomas Quint

    (Department of Mathematics, University of Nevada, Reno Nevada 89557, USA)

Abstract

We show that if y is an odd integer between 1 and $2^{n}-1$, there is an $n\times n$ bimatrix game with exactly y Nash equilibria (NE). We conjecture that this $2^{n}-1$ is a tight upper bound on the number of NEs in a "nondegenerate" $n\times n$ game.

Suggested Citation

  • Martin Shubik & Thomas Quint, 1997. "A Theorem on the Number of Nash Equilibria in a Bimatrix Game," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(3), pages 353-359.
    • Handle: RePEc:spr:jogath:v:26:y:1997:i:3:p:353-359
    Note: Received June 1994 Revised version February 1996
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    Cited by:

    1. Christian Bidard & Guido Erreygers, 1998. "The number and type of long-term equilibria," Journal of Economics, Springer, vol. 67(2), pages 181-205, June.

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