How to make sense of the com M on P ri or assumption under incomplete information

International Journal of Game Theory 28 (3):409-434 (1999)
The Common Prior Assumption (CPA) is central to the economics of information and the foundations of game theory. Recent contributions (Dekel and Gul, 1997, Gul, 1996, Lipman, 1995) have questioned its meaningfulness in situations of incomplete information where there is no ex ante stage and the primitives of the model are the individuals’ belief hierarchies. We address this conceptual issue by providing characterizations of two local versions of the CPA which are in terms of the primitives and, therefore, do not involve a counterfactual and problematic ex ante stage. The characterizations involve three notions: Comprehensive Agreement, no error of beliefs and common belief in no error. Comprehensive Agreement is defined as the absence of “agreement to disagree” about any aspect of beliefs; it is a generalization of Aumann’s (1976) notion of agreement. The entire analysis is carried out locally, that is, with reference to the “true state” (which represents the actual profile of belief hierarchies) and does not rely on the Truth Axiom for individual beliefs.
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