A FURTHER GENERALIZATION OF THE KAKUTANI FIXED POINT THEOREM, WITH APPLICATION TO NASH EQUILIBRIUM POINTS

Abstract

Kakutani's Fixed Point Theorem states that in Euclidean n-space a closed point to (non-void) convex set map of a convex compact set into itself has a fixed point. Kakutani showed that this implied the minimax theorem for finite games. The object of this note is to point out that Kakutani's theorem may be extended to convex linear topological spaces, and implies the minimax theorem for continuous games with continuous payoff as well as the existence of Nash equilibrium points.

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Document Details

Document Type
Technical Report
Publication Date
Feb 09, 1951
Accession Number
AD0603907

Entities

People

  • I. L. Glicksberg

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Convex Sets
  • Geometry
  • Interpolation
  • Mathematical Analysis
  • Mathematics
  • Point Theorem
  • Theorems
  • Topology

Readers

  • Game Theory.
  • Graph Algorithms and Convex Optimization.

Technology Areas

  • Space