Are the players in an interactive belief model meta-certain of the model itself?

Are the players “commonly certain” of an interactive belief model itself? The paper formalizes what it means by: “a player is certain of her own belief-generating map” or “the players are certain of their belief-generating maps (i.e., the model).” The paper shows: a player is certain of her own belief-generating map if and only if her beliefs are introspective. The players are commonly 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. A negative implication of the latter result is that, under common certainty of the model, mutual and common beliefs coincide with each other. This paper then asks whether the “meta-common-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 certain only of her own strategy and belief-generating map.