Bayesian Decision Making in Groups is Hard
Operations Research, https://doi.org/10.1287/opre.2020.2000
43 Pages Posted: 20 Oct 2017 Last revised: 25 Jan 2021
Date Written: October 19, 2017
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: Suggested Citation