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A Note on Nash Equilibrium andFixed Point Theorems

Author

Listed:
  • Hannu Salonen

    (University of Turku)

  • Mitri Kitti

    (University of Turku)

Abstract

We give a proof of the existence of a Nash equilibrium forn-personnormal form games when each player’s utility function is continuousw.r.t. strategy profiles, and concave and differentiable w.r.t. his ownstrategy. The proof uses only elementary mathematical tools such asmathematical induction. We show that this equilibrium existence re-sult is sufficiently general to imply the Brouwer Fixed Point Theorem.The Kakutani Fixed Point Theorem is obtained as a corollary by usingstandard techniques.

Suggested Citation

  • Hannu Salonen & Mitri Kitti, 2019. "A Note on Nash Equilibrium andFixed Point Theorems," Discussion Papers 131, Aboa Centre for Economics.
    • Handle: RePEc:tkk:dpaper:dp131
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    File URL: http://ace-economics.fi/kuvat/dp131.pdf
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    More about this item

    Keywords

    Nash equilibrium; fixed-point theorem;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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