Inductive Proof of a Saddle Point Theorem

Many proofs have been published for the minimax theorem, and all the published inductive proofs have been indirect ones. It has been pointed out that a direct inductive proof is needed, especially for instructional purposes, since indirect proofs are more or less implicit in nature. Such a direct proof is given in [4]: Now the minimax theorem can be stated equivalently in terms of saddle point. And it is the object of the present paper to give a direct inductive proof for the saddle point version of this theorem.