Minimax Theorem

Theorem

Let $G$ be a two-person game.

Let each player $\text A$ and $\text B$ adopt their best mixed strategy.

Then the expected gain of $\text A$ will exactly equal the expected loss of $\text B$.

This gain or loss will then be the value of $G$.

Proof

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Historical Note

The Minimax Theorem was demonstrated by John von Neumann in $1928$.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): game theory
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): game theory