Gibbs lemma
[FILE:Josiah Willard Gibbs -from MMS-.jpg|thumb|200px|Josiah Willard Gibbs]
In game theory and in particular the study of Blotto games and operational research, the Gibbs lemma is a result that is useful in maximization problems. It is named for Josiah Willard Gibbs.
Consider. Suppose is maximized, subject to and, at. If the are differentiable, then the Gibbs lemma states that there exists a such that