Stable Marriage Theorem

The Stable Marriage Theorem states that in a matching problem, such as pairing individuals from two groups (like men and women), there is always a way to match everyone so that no two people would prefer to be with each other over their current partners. This means the matching is "stable," with no incentive for anyone to leave their assigned partner for someone else, ensuring an arrangement where no pair would want to change the match after it's made. The theorem guarantees such a stable configuration exists and can be found through specific algorithms.