The Level Set Method of Joo and its Use in Minimax Theory

15 Pages Posted: 28 Oct 2004

See all articles by J. B. G. Frenk

J. B. G. Frenk

Erasmus University, Rotterdam (EUR) - Department of Econometrics ; Erasmus University, Rotterdam (EUR) - Erasmus Research Institute of Management (ERIM)

G. Kassay

Babes-Bolyai University - Faculty of Mathematics and Computer Science

Date Written: June 2004

Abstract

In this paper we discuss the level set method of Joo and how to use it to give an elementary proof of the well-known Sion's minimax result. Although this proof technique is initiated by Joo and based on the inter-section of upper level sets and a clever use of the topological notion of connectedness, it is not very well known and accessible for researchers in optimization. At the same time we simplified the original proof of Joo and give a more elementary proof of the celebrated Sion's minimax theorem.

Keywords: level set method, minimax theorem, game theory

JEL Classification: M, M11, R4, C61

Suggested Citation

Frenk, J.B.G. (Hans) and Kassay, G., The Level Set Method of Joo and its Use in Minimax Theory (June 2004). Available at SSRN: https://ssrn.com/abstract=611842

J.B.G. (Hans) Frenk (Contact Author)

Erasmus University, Rotterdam (EUR) - Department of Econometrics ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands
+31 0 10 408 1257 (Phone)
+31 0 10 408 9162 (Fax)

Erasmus University, Rotterdam (EUR) - Erasmus Research Institute of Management (ERIM)

P.O. Box 1738
3000 DR Rotterdam
Netherlands

G. Kassay

Babes-Bolyai University - Faculty of Mathematics and Computer Science ( email )

Str. Mihail Kogalniceanu nr. 1
Cluj-Napoca, RO-400,084
Romania

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