## 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 by John von Neumann in 1928.

Formally, let and be Mixed Strategies 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 also turns out that if there is more than one optimal Mixed Strategy, there are infinitely many.