Minimax Theorem
Jump to navigation
Jump to search
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
This theorem requires a proof. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |
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