Uncommon knowledge

This dissertation collects four papers on common knowledge and one on introspection principles in epistemic game theory. The first two papers offer a sustained argument against the importance of common knowledge and belief in explaining social behavior. Chapters 3 and 4 study the role of common knowledge of tautologies in standard models in epistemic logic and game theory. The first considers the problem as it relates to Robert Aumann’s Agreement Theorem; the second (joint work with Peter Fritz) studies it in models of awareness. The fifth paper corrects a claimed Agreement Theorem of Geanakoplos (1989), and exploits the corrected theorem to provide epistemic conditions for correlated equilibrium and Nash equilibrium.