COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1131RRR

Nash and Walras Equilibrium via Brouwer

John Geanakoplos

Revised February 2002

The existence of Nash and Walras equilibrium is proved via Brouwer's Fixed Point Theorem, without recourse to Kakutani's Fixed Point Theorem for correspondences. The domain of the Walras fixed point map is confined to the price simplex, even when there is production and weakly quasi-convex preferences. The key idea is to replace optimization with "satisficing improvement,'' i.e., to replace the Maximum Principle with the "Satisficing Principle.''

Keywords: Equilibrium, Nash, Walras, Brouwer, Kakutani

JEL Classification: C6, C62