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A model of belief influence in large social networks

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  • Antonio Jiménez-Martínez

    (Division of Economics, CIDE)

Abstract

This paper develops a model of evolution of beliefs through communication in an exogenous social network. We assume that the agents are Bayesian updaters and that the network enables them to listen to the opinion of others about some uncertain parameter of interest. We explore the effects of the network on the agents' long-run first-order beliefs about the parameter and investigate the aggregation of private information in large societies. Each agent observes private signals about the value of the unknown parameter and, according to his connections in the network, receives private messages from others as well. A message conveys some information about the signal observed by the sender and about the messages that the sender receives from other indirectly connected agents. The informativeness of a message is not strategically chosen but it is exogenously given by the intensity of the connection. Both signals and messages are independent and identically distributed across time but not necessarily across agents. We first characterize the long-run behavior of an agent's beliefs in terms of some entropy-based measures of the conditional distributions of signals and messages available to the agent. Then, we show that the achievement of a consensus in the society is closely related to the presence of prominent agents who are able to change the evolution of other agents' opinions over time. Finally, we show that the influence of the prominent agents must not be very high in order for the agents to aggregate correctly their private sources of information in the long-run.

Suggested Citation

  • Antonio Jiménez-Martínez, 2014. "A model of belief influence in large social networks," Working Papers DTE 572, CIDE, División de Economía.
    • Handle: RePEc:emc:wpaper:dte572
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    References listed on IDEAS

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    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. Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2013. "Entropy and the Value of Information for Investors," American Economic Review, American Economic Association, vol. 103(1), pages 360-377, February.
    3. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    4. Steiner, Jakub & Stewart, Colin, 2011. "Communication, timing, and common learning," Journal of Economic Theory, Elsevier, vol. 146(1), pages 230-247, January.
    5. Arthur Campbell, 2014. "Signaling in social network and social capital formation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(2), pages 303-337, October.
    6. 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.
    7. Abhijit Banerjee & Arun G Chandrasekhar & Esther Duflo & Mathew O. Jackson, 2014. "Gossip: Identifying Central Individuals in a Social Network," Working Papers id:5925, eSocialSciences.
    8. 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.
    9. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
    10. Parikh, Rohit & Krasucki, Paul, 1990. "Communication, consensus, and knowledge," Journal of Economic Theory, Elsevier, vol. 52(1), pages 178-189, October.
    11. Emanuela Sciubba, 2005. "Asymmetric information and survival in financial markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(2), pages 353-379, February.
    12. repec:hal:pseose:hal-00812682 is not listed on IDEAS
    13. Matthew O. Jackson & Tomas Rodriguez-Barraquer & Xu Tan, 2012. "Social Capital and Social Quilts: Network Patterns of Favor Exchange," American Economic Review, American Economic Association, vol. 102(5), pages 1857-1897, August.
    14. Daron Acemoglu & Asuman Ozdaglar, 2011. "Opinion Dynamics and Learning in Social Networks," Dynamic Games and Applications, Springer, vol. 1(1), pages 3-49, March.
    15. Peter M. DeMarzo & Dimitri Vayanos & Jeffrey Zwiebel, 2003. "Persuasion Bias, Social Influence, and Unidimensional Opinions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 118(3), pages 909-968.
    16. Koessler, Frederic, 2001. "Common knowledge and consensus with noisy communication," Mathematical Social Sciences, Elsevier, vol. 42(2), pages 139-159, September.
    17. Martin W. Cripps & Jeffrey C. Ely & George J. Mailath & Larry Samuelson, 2008. "Common Learning," Econometrica, Econometric Society, vol. 76(4), pages 909-933, July.
    18. Azomahou, T. & Opolot, D., 2014. "Beliefs dynamics in communication networks," MERIT Working Papers 2014-034, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    19. , & , & ,, 2016. "Fragility of asymptotic agreement under Bayesian learning," Theoretical Economics, Econometric Society, vol. 11(1), January.
    20. Martin Cripps & Jeffrey Ely & George Mailath & Larry Samuelson, 2013. "Common learning with intertemporal dependence," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 55-98, February.
    21. Daron Acemoğlu & Giacomo Como & Fabio Fagnani & Asuman Ozdaglar, 2013. "Opinion Fluctuations and Disagreement in Social Networks," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 1-27, February.
    22. Galeotti, Andrea & Ghiglino, Christian & Squintani, Francesco, 2013. "Strategic information transmission networks," Journal of Economic Theory, Elsevier, vol. 148(5), pages 1751-1769.
    23. Heifetz, Aviad, 1996. "Comment on Consensus without Common Knowledge," Journal of Economic Theory, Elsevier, vol. 70(1), pages 273-277, July.
    24. Crawford, Vincent P & Sobel, Joel, 1982. "Strategic Information Transmission," Econometrica, Econometric Society, vol. 50(6), pages 1431-1451, November.
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    Cited by:

    1. Jiménez-Martínez, Antonio & Melguizo-López, Isabel, 2022. "Making friends: The role of assortative interests and capacity constraints," Journal of Economic Behavior & Organization, Elsevier, vol. 203(C), pages 431-465.
    2. James C. D. Fisher & John Wooders, 2017. "Interacting information cascades: on the movement of conventions between groups," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 211-231, January.

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    More about this item

    Keywords

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

    JEL classification:

    • 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
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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