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

by Irving Leonard Glicksberg

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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.

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