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

Abstract

In an interactive belief model, are the players"commonly meta-certain"of the model itself? This paper formalizes such implicit"common meta-certainty"assumption. To that end, the paper expands the objects of players' beliefs from events to functions defined on the underlying states. Then, the paper defines a player's belief-generating map: it associates, with each state, whether a player believes each event at that state. 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 an epistemic characterization of game-theoretic solution concepts. The paper shows: if each player is logical and (meta-)certain of her own strategy and belief-generating map, then each player correctly believes her own rationality. Consequently, common belief in rationality alone leads to actions that survive iterated elimination of strictly dominated actions.