Okayama Economic Review
Published by the Economic Association of Okayama University

Online ISSN 2433-4146
Print ISSN 0386-3069


藤本 喬雄
石山 健一
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.
研究ノート (Note)