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The Dynamics of Continuous Cultural Traits in Social Networks

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  • Büchel, Berno

    (Center for Mathematical Economics, Bielefeld University)

  • Hellmann, Tim

    (Center for Mathematical Economics, Bielefeld University)

  • Pichler, Michael

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We consider an OLG model (of a socialization process) where continuous traits are transmitted from an adult generation to the children. A weighted social network describes how children are influenced not only by their parents but also by other role models within the society. Parents can invest into the purposeful socialization of their children by strategically displaying a cultural trait (which need not coincide with their true trait). Based on Nash equilibrium behavior, we study the dynamics of cultural traits throughout generations. We provide conditions on the network structure that are sufficient for long–run convergence to a society with homogeneous subgroups. In the special case of quadratic utility, the condition is that each child is more intensely shaped by its parents than by the social environment. Our model also represents an extension of the classical DeGroot model of opinion formation for which we introduce strategic interaction in choice of expressed opinions (in our setup: traits). We show that under strategic interaction convergence is slower and for convergence we need more restrictive necessary and sufficient conditions than in the DeGroot model.

Suggested Citation

  • Büchel, Berno & Hellmann, Tim & Pichler, Michael, 2016. "The Dynamics of Continuous Cultural Traits in Social Networks," Center for Mathematical Economics Working Papers 457, Center for Mathematical Economics, Bielefeld University.
  • Handle: RePEc:bie:wpaper:457
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    File URL: https://pub.uni-bielefeld.de/download/2900980/2900981
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    References listed on IDEAS

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    Cited by:

    1. Förster, Manuel & Grabisch, Michel & Rusinowska, Agnieszka, 2013. "Anonymous social influence," Games and Economic Behavior, Elsevier, vol. 82(C), pages 621-635.
    2. Prummer, Anja & Siedlarek, Jan-Peter, 2014. "Institutions And The Preservation Of Cultural Traits," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 470, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    3. Grabisch, Michel & Rusinowska, Agnieszka, 2013. "A model of influence based on aggregation functions," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 316-330.
    4. repec:gam:jgames:v:8:y:2017:i:4:p:51-:d:119855 is not listed on IDEAS
    5. Buechel, Berno & Hellmann, Tim & Klößner, Stefan, 2015. "Opinion dynamics and wisdom under conformity," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 240-257.
    6. Olcina, Gonzalo & Panebianco, Fabrizio & Zenou, Yves, 2017. "Conformism, Social Norms and the Dynamics of Assimilation," CEPR Discussion Papers 12166, C.E.P.R. Discussion Papers.
    7. Hellmann, Tim & Panebianco, Fabrizio, 2018. "The transmission of continuous cultural traits in endogenous social networks," Center for Mathematical Economics Working Papers 579, Center for Mathematical Economics, Bielefeld University.
    8. Cheung, Man-Wah & WU, JIABIN, 2016. "On The Transmission of Continuous Cultural Traits," MPRA Paper 69934, University Library of Munich, Germany.
    9. Anja Prummer & Jan-Peter Siedlarek, 2016. "Community Leaders and the Preservation of Cultural Traits," Working Papers 806, Queen Mary University of London, School of Economics and Finance.
    10. repec:eee:gamebe:v:105:y:2017:i:c:p:155-176 is not listed on IDEAS
    11. Prummer, Anja & Siedlarek, Jan-Peter, 2017. "Community leaders and the preservation of cultural traits," Journal of Economic Theory, Elsevier, vol. 168(C), pages 143-176.
    12. Panebianco, Fabrizio & Verdier, Thierry, 2017. "Paternalism, homophily and cultural transmission in random networks," Games and Economic Behavior, Elsevier, vol. 105(C), pages 155-176.
    13. Michel Grabisch & Antoine Mandel & Agnieszka Rusinowska & Emily Tanimura, 2015. "Strategic influence in social networks," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01158168, HAL.
    14. Panebianco, Fabrizio & Verdier, Thierry, 2015. "Paternalism, Cultural Transmission and Diffusion on Complex Networks," CEPR Discussion Papers 10722, C.E.P.R. Discussion Papers.
    15. repec:hal:cesptp:halshs-00906367 is not listed on IDEAS
    16. repec:eee:jetheo:v:174:y:2018:i:c:p:300-323 is not listed on IDEAS
    17. Manuel Förster & Michel Grabisch & Agnieszka Rusinowska, 2012. "Ordered Weighted Averaging in Social Networks," Documents de travail du Centre d'Economie de la Sorbonne 12056, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    18. Yann Algan & Pierre Cahuc, 2010. "Inherited Trust and Growth," American Economic Review, American Economic Association, vol. 100(5), pages 2060-2092, December.
    19. Michel Grabisch & Alexis Poindron & Agnieszka Rusinowka, 2017. "A model of anonymous influence with anti-conformist agents," Documents de travail du Centre d'Economie de la Sorbonne 17047, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    20. repec:eee:ecolet:v:167:y:2018:i:c:p:51-55 is not listed on IDEAS
    21. Del Bello, Carlo & Panebianco, Fabrizio & Verdier, Thierry & Zenou, Yves, 2016. "Cultural Transmission and Socialization Spillovers in Education," CEPR Discussion Papers 11419, C.E.P.R. Discussion Papers.

    More about this item

    Keywords

    cultural transmission; social networks; preference formation; cultural persistence; opinion dynamics;

    JEL classification:

    • A14 - General Economics and Teaching - - General Economics - - - Sociology of Economics
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • Z13 - Other Special Topics - - Cultural Economics - - - Economic Sociology; Economic Anthropology; Language; Social and Economic Stratification

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