Are the Players in an Interactive Belief Model Meta-certain of the Model Itself?

Are the players “commonly meta-certain” of an interactive belief model itself? The paper formalizes what it means by: “a player is (meta-)certain of her own belief-generating map” or “the players are (meta-)certain of the profile of belief-generating maps (i.e., the model).” The paper shows: a player is (meta-)certain of her own belief-generating map if and only if her beliefs are introspective. The players are commonly (meta-)certain of the model if and only if, for any event which some player i believes at some state, it is common belief at the state that player i believes the event. This paper then asks whether the “common meta-certainty” assumption is needed for epistemic characterizations of game-theoretic solution concepts. The paper shows: common belief in rationality leads to actions that survive iterated elimination of strictly dominated actions, as long as each player is logical and (meta-)certain only of her own strategy and belief-generating map