Bayesian Decision Making in Groups is Hard
This reveals fundamental computational barriers in group decision-making for AI and social science, indicating that even rational agents face intractable problems in exchanging opinions.
The paper tackles the computational complexity of Bayesian decision-making in networked agents, showing that computing rational posterior beliefs and actions is NP-hard for two natural utility functions, and even approximating these beliefs is hard.
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.