Sufficient conditions for Nash equilibrium in an n-person game are given in terms
of what the players know and believe - about the game, and about each other's rationality,
actions, knowledge, and beliefs. Mixed strategies are treated not as conscious randomizations,
but as conjectures, on the part of other players, as to what a player will do. Common
knowledge plays a smaller role in characterizing Nash equilibrium than had been supposed.
When n=2, mutual knowledge of the payoff functions, of rationality, and of the
conjectures implies that the conjectures form a Nash equilibrium. When n (greater
than or equal to) 3 and there is a common prior, mutual knowledge of the payoff functions
and of rationality, and common knowledge of the conjectures, imply that the conjectures
form a Nash equilibrium. Examples show the results to be tight.