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

Satoshi Fukuda
(Department of Decision Sciences and IGIER, Bocconi University)

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.

In Joseph Halpern and Andrés Perea: Proceedings Eighteenth Conference on Theoretical Aspects of Rationality and Knowledge (TARK 2021), Beijing, China, June 25-27, 2021, Electronic Proceedings in Theoretical Computer Science 335, pp. 155–170.
Published: 22nd June 2021.

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