Minimax Theorem
The fundamental theorem of Game Theory which states that every Finite, Zero-Sum, two-person Game has optimal Mixed Strategies. It was proved byJohn von Neumann 
in 1928.
Formally, let 
and 
be MixedStrategies for players A and B. Let 
be the Payoff Matrix. Then
where
is called the Value of the Game and and are called the solutions. It alsoturns out that if there is more than one optimal Mixed Strategy, there are infinitely many.See also Mixed Strategy
References
Willem, M. Minimax Theorem. Boston, MA: Birkhäuser, 1996.
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