Common priors under incomplete information: a unification

While the meaningfulness of the common prior assumption (CPA) under incomplete information has been established recently by various authors, its epistemic rationale has not yet been adequately clarified. To do so, we provide a characterization of the CPA in terms of a new condition called "Mutual Calibration", and argue that it constitutes a more transparent and more primitive formalization of the Harsanyi Doctrine than the existing characterizations. Our analysis unifies the understanding of the CPA under incomplete information and clarifies the role of higher-order expectations and of the difference between situations with only two and those with at least three agents. In the concluding section, the analysis is applied to the problem of defining Bayesian consistency of the intertemporal beliefs of a single-agent with imperfect memory. The CPA yields a notion of "Bayesian updating without a prior".