28 Pages Posted: 3 Jun 2017 Last revised: 16 Dec 2017
Date Written: August 31, 2017
We study higher-order expectations paralleling the Harsanyi (1968) approach to higher-order beliefs — taking a basic set of random variables as given, and building up higher-order expectations from them. We report three main results. First, we generalize Samet's (1998a) characterization of the common prior assumption in terms of higher-order expectations, resolving an apparent paradox raised by his result. Second, we characterize when the limits of higher-order expectations can be expressed in terms of agents' heterogeneous priors, generalizing Samet's expression of limit higher-order expectations via the common prior. Third, we study higher-order average expectations — objects that arise in network games. We characterize when and how the network structure and agents' beliefs enter in a separable way.
Keywords: higher-order beliefs, higher-order expectations, networks, common prior, heterogeneous priors
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