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Bayesian Decision Making in Groups is Hard

Author

Listed:
  • Jan Hązła

    (Institutes of Mathematics and Computer Science, École polytechnique fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland;)

  • Ali Jadbabaie

    (Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139;)

  • Elchanan Mossel

    (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139;)

  • M. Amin Rahimian

    (Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15260)

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.

Suggested Citation

  • Jan Hązła & Ali Jadbabaie & Elchanan Mossel & M. Amin Rahimian, 2021. "Bayesian Decision Making in Groups is Hard," Operations Research, INFORMS, vol. 69(2), pages 632-654, March.
    • Handle: RePEc:inm:oropre:v:69:y:2021:i:2:p:632-654
    DOI: 10.1287/opre.2020.2000
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    References listed on IDEAS

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