Bayesian Decision Making in Groups is Hard

Operations Research, Forthcoming

43 Pages Posted: 20 Oct 2017 Last revised: 15 Feb 2020

See all articles by Jan Hązła

Jan Hązła

Massachusetts Institute of Technology (MIT)

Ali Jadbabaie

Institute for Data, Systems, and Society, Massachusetts Institute of Technology

Elchanan Mossel

Massachusetts Institute of Technology (MIT)

M. Amin Rahimian

University of Pitttsburgh; Massachusetts Institute of Technology (MIT)

Date Written: October 19, 2017

Abstract

We study the computations that Bayesian agents undertake when exchanging opinions over a network. The agents act repeatedly on their private information and take myopic actions that maximize their expected utility according to a fully rational posterior belief. We show that such computations are NP-hard for two natural utility functions: one with binary actions, and another where agents reveal their posterior beliefs. In fact, we show that distinguishing between posteriors that are concentrated on different states of the world is NP-hard. Therefore, even approximating the Bayesian posterior beliefs is hard. We also describe a natural search algorithm to compute agents' actions, which we call elimination of impossible signals, and show that if the network is transitive, the algorithm can be modified to run in polynomial time.

Keywords: Observational Learning, Bayesian Decision Theory, Computational Complexity, Group Decision-Making, Computational Social Choice, Inference over Graphs

JEL Classification: D83, D85

Suggested Citation

Hązła, Jan and Jadbabaie, Ali and Mossel, Elchanan and Rahimian, M. Amin, Bayesian Decision Making in Groups is Hard (October 19, 2017). Operations Research, Forthcoming, Available at SSRN: https://ssrn.com/abstract=3055954 or http://dx.doi.org/10.2139/ssrn.3055954

Jan Hązła

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

Ali Jadbabaie

Institute for Data, Systems, and Society, Massachusetts Institute of Technology ( email )

77 Massachusetts Ave E18-309C
E18-309C
02139, MA MA 02139
United States
6172537339 (Phone)
6172537339 (Fax)

HOME PAGE: http://web.mit.edu/www/jadbabai

Elchanan Mossel

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

M. Amin Rahimian (Contact Author)

University of Pitttsburgh ( email )

135 N Bellefield Ave
Pittsburgh, PA 15260
United States

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

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