Okayama Economic Review

Published by the Economic Association of Okayama University
Fujimoto, Takao

Ishiyama, Ken-ichi

Abstract

This note is to prove Tucker's theorem on linear inequalities based on the proof method of minimax theorems which uses Kakutani's fixed point theorem. One device is necessary to convert the minimax theorems to Tucker's formulation. This is a slight restriction on the image sets when creating a set-valued map. We also present nonlinear generalizations of Tucker's theorem employing the same method. All we need is that the set of variable values for which an objective function attains its maximum is convex. This objective function is a convex combination of functions. We also present a proof of the fact that a local characterization of inequality systems, when a given mapping is differentiable, can be made global provided the mapping is concave.

Note

研究ノート (Note)

ISSN

0386-3069

NCID

AN00032897

NAID