Bayesian Decision Making in Groups is Hard

• Published in: arXiv.org
• Main Authors: Hązła, Jan, Jadbabaie, Ali, Mossel, Elchanan, M Amin Rahimian
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 27.07.2019
• Subjects: Bayesian analysis; Computer Science - Computational Complexity; Computer Science - Learning; Computer Science - Multiagent Systems; Computer Science - Social and Information Networks; Decision making; Economic models; Expected utility; Mathematics - Statistics Theory; Polynomials; Search algorithms; Statistics - Theory
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1705.04770

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.