| Authors | زینب سلطانی رنانی |
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| Conference Title | the 4th International Conference on Computational Algebra, Computational Number Theory and Applications |
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| Holding Date of Conference | 2023-07-04 - 2023-07-06 |
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| Event Place | 1 - کاشان |
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| Presented by | دانشگاه کاشان |
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| Presentation | SPEECH |
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| Conference Level | International Conferences |
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Abstract
Techniques and principles of Minimax theory play a key role in
many areas of research, including game theory, optimization. Arguably the
most important result in zero-sum games, the Minimax Theorem was stated
by John von Neumann in 1928 which was considered the starting point of
game theory.
Formally, von Neumann’s minimax theorem states:
Let X ⊂ Rn and Y ⊂ Rm be compact convex sets. If f : X × Y → R is a
continuous function that is concave-convex, i.e.
(1) f (·, y) : X → R is concave for fixed y , and
(2) f (x, ·) : Y → R is convex for fixed x.
Then
max
x∈X min
y∈Y f (x, y) = min
y∈Y max
x∈X f (x, y).
In this paper, By using asymptotic function, as the main result, we prove
Minimax Theorem under weaker assumptions of continuity and convexity,
when the feasible set is an unbounded
