Aumann was the first to define the concept of correlated equilibrium in game theory, which is a type of equilibrium in non-cooperative games that is more flexible than the classical Nash equilibrium. Furthermore, Aumann has introduced the first purely formal account of the notion of common knowledge in game theory. He collaborated with Lloyd Shapley on the Aumann–Shapley value. He is also known for his agreement theorem, in which he argues that under his given conditions, two Bayesian rationalists with common prior beliefs cannot agree to disagree.