CFDP 1131R2

Nash and Walras Equilibrium via Brouwer

Author(s): 

Publication Date: August 1996

Revision Date: June 2001

Pages: 17

Abstract: 

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 Codes:  C6, C62