CFDP Revision Date
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-concave preferences. The key idea is to replace optimization with “satisﬁcing improvement,” i.e., to replace the Maximum Principle with the “Satisﬁcing Principle.”
Geanakoplos, John, "Nash and Walras Equilibrium Via Brouwer" (1996). Cowles Foundation Discussion Papers. 1377.