Pure self-confirming equilibrium

In a Self-Confirming Equilibrium (Fudenberg and Levine, 1993A) every player obtains partial information about other players' strategies and plays a best response to some conjecture which is consistent with his information. Two kinds of information structures are considered: In the first each player observes his own payoff while in the second the information is the distribution of players among the various actions. For each of these information structures we prove that pure Self-Confirming Equilibrium exists in some classes of games. Pure Nash equilibrium may fail to exist in these classes.