Knowledge in games

• Properties of Knowledge Operator: truth (a player can only know something that is true), necessitation (a player knows the state space), inference, negative introspection (no unknown unknowns) and positive introspection (a player knows own information structure)
• An event is self-evident between players A and B if, whenever it occurs, both players know it
• If two players hold identical beliefs about the world so that any differences in beliefs is due to differences in information, they cannot agree to disagree
• common knowledge of rationality implies rationalizability
• if beliefs are derived from a common prior and players are rational in every state, then we obtain a correlated equilibrium