An Elementary Proof of a Minimax Theorem

TL;DR

This paper provides a straightforward, self-contained proof of Fan's minimax theorem suitable for teaching advanced undergraduates, simplifying Nikaido's approach.

Contribution

It offers an elementary, accessible proof of a classical minimax theorem, making it easier to teach and understand at the undergraduate level.

Findings

Simplified proof of Fan's minimax theorem

Self-contained and easy to teach in undergraduate courses

Based on Nikaido's argument with improvements

Abstract

Here, we give a self-contained and elementary proof of a minimax theorem due to Fan in a simplified setting that can be taught in an advanced undergraduate course. Our proof follows Nikaido's argument with some simplifications.