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Uniqueness of the index for Nash equilibria of two-player games

Author

Listed:
  • Robert Wilson

    (Business School, Stanford University, Stanford, CA 94305-5015, USA)

  • Srihari Govindan

    (Economics Department, University of Western Ontario, London, Ontario N6A 5C2, CANADA)

Abstract

Given a map whose roots are the Nash equilibria of a game, each component of the equilibrium set has an associated index, defined as the local degree of the map. This note shows that for a two-player game, every map with the same roots induces the same index. Moreover, this index agrees with the Shapley index constructed from the Lemke-Howson algorithm.

Suggested Citation

  • Robert Wilson & Srihari Govindan, 1997. "Uniqueness of the index for Nash equilibria of two-player games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(3), pages 541-549.
    • Handle: RePEc:spr:joecth:v:10:y:1997:i:3:p:541-549
    Note: Received: May 30, 1996; revised version June 25, 1996
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    Cited by:

    1. Demichelis, Stefano & Germano, Fabrizio, 2002. "On (un)knots and dynamics in games," Games and Economic Behavior, Elsevier, vol. 41(1), pages 46-60, October.
    2. DeMichelis, Stefano & Germano, Fabrizio, 2000. "On the Indices of Zeros of Nash Fields," Journal of Economic Theory, Elsevier, vol. 94(2), pages 192-217, October.
    3. Hauk, Esther & Hurkens, Sjaak, 2002. "On Forward Induction and Evolutionary and Strategic Stability," Journal of Economic Theory, Elsevier, vol. 106(1), pages 66-90, September.

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