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Social activity and network formation

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  • Baetz, Oliver

    ()
    (Department of Economics, University of Cambridge)

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    Abstract

    This paper develops a simple model in which a social hierarchy emerges endogenously when agents form a network for complementary interaction (``activity''). Specifically, we assume that agents are ex ante identical and their best response activity, as well as their value function, increases (strictly) concavely in the total activity of their neighbours in the network. There exists a unique and stable positive activity equilibrium on exogenous networks under mild conditions. When we endogenise network formation, equilibria become strongly structured: more active players have more neighbours, i.e. a higher degree, but tend to sponsor fewer links. Additionally, in strict equilibria agents separate themselves into groups characterised by the symmetric activity of their members. The characteristic activity decreases in group size and the network is a complete multipartite graph.

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    Bibliographic Info

    Article provided by Econometric Society in its journal Theoretical Economics.

    Volume (Year): (Forthcoming)
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    Handle: RePEc:the:publsh:1487

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    Web page: http://econtheory.org

    Related research

    Keywords: Network formation; strategic complementarity; supermodularity; peer effects; social hierarchy;

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    References

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    1. Vives, X., 1988. "Nash Equilibrium With Strategic Complementarities," UFAE and IAE Working Papers 107-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    2. Matthew O. Jackson & Asher Wolinsky, 1994. "A Strategic Model of Social and Economic Networks," Discussion Papers 1098, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Jackson, Matthew O. & Watts, Alison, 2002. "On the formation of interaction networks in social coordination games," Games and Economic Behavior, Elsevier, vol. 41(2), pages 265-291, November.
    4. Calvó-Armengol, Antoni & Zenou, Yves, 2003. "Social Networks and Crime Decisions: The Role of Social Structure in Facilitating Delinquent Behaviour," CEPR Discussion Papers 3966, C.E.P.R. Discussion Papers.
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    6. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
    7. Andrea Galeotti & Sanjeev Goyal, 2007. "The Law of the Few," Economics Discussion Papers 636, University of Essex, Department of Economics.
    8. Bramoulle, Yann & Kranton, Rachel, 2007. "Public goods in networks," Journal of Economic Theory, Elsevier, vol. 135(1), pages 478-494, July.
    9. Sanjeev Goyal & Fernando Vega-Redondo, 2003. "Network Formation and Social Coordination," Working Papers 481, Queen Mary, University of London, School of Economics and Finance.
    10. Mohamed Belhaj & Yann Bramoullé & Frédéric Deroïan, 2012. "Network Games under Strategic Complementarities," Working Papers halshs-00793439, HAL.
    11. Glaeser, Edward L & Sacerdote, Bruce & Scheinkman, Jose A, 1996. "Crime and Social Interactions," The Quarterly Journal of Economics, MIT Press, vol. 111(2), pages 507-48, May.
    12. Coralio Ballester & Antoni Calvo-Armengol & Yves Zenou, 2005. "Who's Who in Networks. Wanted: the Key Player," NajEcon Working Paper Reviews 666156000000000586, www.najecon.org.
    13. Antoni Calv�-Armengol & Eleonora Patacchini & Yves Zenou, 2009. "Peer Effects and Social Networks in Education," Review of Economic Studies, Oxford University Press, vol. 76(4), pages 1239-1267.
    14. Patacchini, Eleonora & Zenou, Yves, 2008. "The strength of weak ties in crime," European Economic Review, Elsevier, vol. 52(2), pages 209-236, February.
    15. Timo Hiller & Timo Hiller, 2013. "Peer Effects in Endogenous Networks," STICERD - Theoretical Economics Paper Series /2013/564, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    16. Jens Ludwig & Greg J. Duncan & Paul Hirschfield, 2001. "Urban Poverty And Juvenile Crime: Evidence From A Randomized Housing-Mobility Experiment," The Quarterly Journal of Economics, MIT Press, vol. 116(2), pages 655-679, May.
    17. John Kennan, 2001. "Uniqueness of Positive Fixed Points for Increasing Concave Functions on Rn: An Elementary Result," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 4(4), pages 893-899, October.
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