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Consensus in Communication Networks under Bayesian Updating

Author

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  • Antonio Jiménez-Martínez

    (Division of Economics, CIDE)

Abstract

This paper studies the evolution of beliefs of a group of Bayesian updaters who are connected through a social network that enables them to listen to the opinions of others. Each agent observes a sequence of private signals about the value of an unknown parameter. In addition, the agent receives private messages from others according to her connections in the network. A message conveys some information about the signal observed by the sender. Both signals and messages are independent and identically distributed across time but not necessarily across agents. Messages cannot be transmitted through indirect connections in the network. We first characterize the long-run behavior of an agent's beliefs in terms of the relative entropies of the conditional distributions of signals and messages available to the agent. Then, under some mild assumptions on the distributions of signals and messages, we identify a condition under which the agents reach a consensus in their opinions even when they begin with different priors. Finally, in contrast with most results in the existing literature, we show that a consensus need not be reached in a strongly connected network.

Suggested Citation

  • Antonio Jiménez-Martínez, 2012. "Consensus in Communication Networks under Bayesian Updating," Working Papers DTE 529, CIDE, División de Economía.
    • Handle: RePEc:emc:wpaper:dte529
    as

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    File URL: http://www.economiamexicana.cide.edu/RePEc/emc/pdf/DTE/DTE529.pdf
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    References listed on IDEAS

    as
    1. Jeanne Hagenbach & Frédéric Koessler, 2010. "Strategic Communication Networks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(3), pages 1072-1099.
    2. Daron Acemoglu & Giacomo Como & Fabio Fagnani & Asuman E. Ozdaglar, 2010. "Opinion Fluctuations and Disagreement in Social Networks," Levine's Working Paper Archive 661465000000000208, David K. Levine.
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    4. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-391, June.
    5. Daron Acemoglu & Munther A. Dahleh & Ilan Lobel & Asuman Ozdaglar, 2011. "Bayesian Learning in Social Networks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(4), pages 1201-1236.
    6. Parikh, Rohit & Krasucki, Paul, 1990. "Communication, consensus, and knowledge," Journal of Economic Theory, Elsevier, vol. 52(1), pages 178-189, October.
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    9. Koessler, Frederic, 2001. "Common knowledge and consensus with noisy communication," Mathematical Social Sciences, Elsevier, vol. 42(2), pages 139-159, September.
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    11. Heifetz, Aviad, 1996. "Comment on Consensus without Common Knowledge," Journal of Economic Theory, Elsevier, vol. 70(1), pages 273-277, July.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Communication networks; Bayesian updating; private signals; private messages; consensus.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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