Definition
Aumann’s Agreement Theorem states that two rational agents (who are Bayesian and have common priors) cannot “agree to disagree” once their opinions are common knowledge. If they know each other’s opinions, they must converge on the same probability for a given event.
Why It Matters
It proves that disagreement between rational agents is usually a sign of hidden information or irrational bias rather than permanent reality. It forces us to seek the underlying reasons why our models of the world don’t converge.
Core Concepts
- Common Priors: The assumption that the agents began with the same initial beliefs before receiving different information.
- Common Knowledge: Not just that A knows X and B knows X, but that A knows that B knows that A knows X, and so on.
- Opinion as Information: A rational agent treats another rational agent’s differing opinion as a signal that the other agent has private information they lack.
- Convergence: In an ideal bayesian world, the process of sharing opinions leads inevitably to consensus.