Abstract
In this paper, we discuss generalized hierarchical minimax theorems with four set-valued mappings and we propose some scalar hierarchical minimax theorems and generalized hierarchical minimax theorems in topological spaces. Some examples are given to illustrate our results.
Highlights
1 Introduction It is well known that minimax theorems are important in the areas of game theory, and mathematical economical and optimization theory
The minimax theorem of two functions has been studied based on the two-person nonzero-sum games; on the other hand, with the development of vector optimization, there are many authors paying their attention to minimax problems of vector-valued mappings
We prove the hierarchical minimax theorem for scalar set-valued mappings
Summary
It is well known that minimax theorems are important in the areas of game theory, and mathematical economical and optimization theory (see [ – ]). Some other minimax theorems for set-valued mappings can be found in [ – ].
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