Speaker: Benjamin Golub Harvard Society of Fellows

Title: Consensus Expectations and Conventions

Joint work with Stephen Morris (Department of Economics, Princeton)

Abstract:

Players have uncertainty over both an external random variable—such as a security price—and over each other's beliefs. We study agents’ subjective expectations of the weighted average of others' subjective expectations . . . of the weighted average of others' subjective expectations of the random variable. The weights can be viewed as a network. By relating iterated average expectations to a Markov chain, we characterize their limit properties. This generalizes prior results on games with common priors and on complete-information network games. We then apply the conclusions to study coordinating on a convention; prices in over-the-counter financial markets; the possibility of rationalizable trade; and the robustness of equilibrium.

First, we show that iterating subjective average expectations corresponds to iterating a Markov matrix and  that there is a common-certainty consensus expectation to which highly iterated average expectations all converge. This generalizes a result of Samet (1998) on the convergence of iterated expectations to ex ante expectations with respect to a common prior; our result is an analogue of his even in cases where a common prior does not exist. 

Second, we characterize consensus expectations.  Under the common prior assumption, consensus expectations correspond to expectations under the common prior, by the argument of Samet (1998).  Under complete information, consensus expectations correspond to an average of players' heterogeneous expectations of the external state, weighted according to their network centralities (Ballester, Calvo-Armengol, and Zenou, 2006). When there is neither a common prior nor complete information, we describe a sense in which only less informed players' prior beliefs play a role in consensus expectations, even when there is almost common certainty of the state. 

Third, we discuss applications where consensus expectations are important.  Consensus expectations determine the convention played in games with linear best response functions that put different weights on others' actions, in the limit where the coordination motive dominates. Consensus expectations also correspond to asset prices in an over-the-counter market with risk-neutral traders and short horizons.  Beyond these applications where consensus applications are of direct interest as an outcome, the theory is used as a tool to derive two other kinds of results. First, we establish new theorems on the impossibility of rationalizable trade with many players. We also study the robustness of equilibria in coordination games, generalizing theorems of Kajii and Morris (1997) to settings without a common prior.

Biography:

Benjamin Golub’s research focuses on microeconomic theory -- and, in particular, social and economic networks: how these networks form when agents invest strategically in relationships, how information is transmitted through them, and how they mediate important economic processes such as group cooperation. Applications of the research include measuring social segregation and understanding its consequences for polarization of beliefs or behaviors.

His current work focuses on (i) the theory of group negotiations (e.g., over pollution) in settings where players' efforts have asymmetric effects on each other's payoffs; and (ii) experimental studies of how social networks lead to contagion of incorrect beliefs or behaviors due to biases in the way individuals process and transmit information.

Golub is currently a Junior Fellow at the Harvard Society of Fellows until June 2015, and will then begin an appointment as an Assistant Professor at the Harvard Department of Economics. He received a Ph.D. in Economics at Stanford (in the Graduate School of Business) in 2012 and a B.S. in Mathematics from the California Institute of Technology in 2007.His research website, with up-to-date publications and other information, is at http://www.bengolub.net.