Higher-Order Expectations

28 Pages Posted: 3 Jun 2017 Last revised: 4 Jun 2017

Benjamin Golub

Harvard University

Stephen Morris

Princeton University - Department of Economics

Date Written: June 3, 2017

Abstract

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

Suggested Citation

Golub, Benjamin and Morris, Stephen, Higher-Order Expectations (June 3, 2017). Available at SSRN: https://ssrn.com/abstract=2979089 or http://dx.doi.org/10.2139/ssrn.2979089

Benjamin Golub (Contact Author)

Harvard University ( email )

Littauer Center, Dept of Economics
1805 Cambridge Street
Cambridge, MA 02138
United States

Stephen Edward Morris

Princeton University - Department of Economics ( email )

Princeton, NJ 08544-1021
United States

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