A Further Generalization of the Kakutani Fixed-Point Theorem, with Applications to Nash Equilibrium Points.

Irving Leonard Glicksberg

Expert InsightsPublished 1951

A proof of the analogue of the Tychonoff extension of the fixed-point theorem of Brouwer for the Kakutani fixed-point theorem. The Kakutani theorem is extended to convex Hausdorff linear topological spaces. With this, the existence of equilibrium points in the general [n]-person continuous game, with continuous payoffs, is demonstrated. 8 pp.

Document Details

  • Copyright: RAND Corporation
  • Availability: Web Only
  • Year: 1951
  • Pages: 8
  • Document Number: P-193

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Glicksberg, Irving Leonard, A Further Generalization of the Kakutani Fixed-Point Theorem, with Applications to Nash Equilibrium Points. Santa Monica, CA: RAND Corporation, 1951. https://www.rand.org/pubs/papers/P193.html.
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