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The dynamics of social interaction with agents’ heterogeneity

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Author Info

  • Emilio Barucci

    ()
    (Department of Mathematics, Politecnico di Milano)

  • Marco Tolotti

    ()
    (Department of Applied Mathematics, University of Venice)

Abstract

We analyze a class of binary dynamic models inspired by [4] on agents’ choices and social interaction. The main feature of our analysis is that agents are heterogeneous, in particular their attitude to interact with the choices of the other agents changes over time endogenously. Although dynamic approaches to the study of models with heterogeneous agents have been already applied in different fields, to our knowledge a complete study of an endogenously varying population of agents has not yet been pursued. As observed in [3], the main problem is given by the fact that with heterogeneous agents the system may be non reversible. We address these problems, we describe the (possible multiple) steady states of the processes involved, we analyze local and global stability and we discuss the similarities and the differences with respect to the literature. Applications are also provided.

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File URL: http://virgo.unive.it/wpideas/storage/2009wp189.pdf
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Bibliographic Info

Paper provided by Department of Applied Mathematics, Università Ca' Foscari Venezia in its series Working Papers with number 189.

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Length: 28 pages
Date of creation: Jul 2009
Date of revision:
Handle: RePEc:vnm:wpaper:189

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Keywords: heterogeneous agent models; intensity-based models; mean field interactions; random utilities; social interactions.;

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References

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  1. repec:att:wimass:9707 is not listed on IDEAS
  2. Allison, G. & Fudenberg, D., 1992. "Rules of Thumb for Social Learning," Working papers 92-12, Massachusetts Institute of Technology (MIT), Department of Economics.
  3. 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.
  4. Edward L. Glaeser & Bruce I. Sacerdote & Jose A. Scheinkman, 2003. "The Social Multiplier," Journal of the European Economic Association, MIT Press, vol. 1(2-3), pages 345-353, 04/05.
  5. Bischi, Gian-Italo & Gallegati, Mauro & Gardini, Laura & Leombruni, Roberto & Palestrini, Antonio, 2006. "Herd Behavior And Nonfundamental Asset Price Fluctuations In Financial Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 10(04), pages 502-528, September.
  6. William A. Brock & Steven N. Durlauf, 1999. "A formal model of theory choice in science," Economic Theory, Springer, vol. 14(1), pages 113-130.
  7. Sah, R.K., 1990. "Social Osmosis And Patterns Of Crime: A Dynamic Economic Analysis," Papers 609, Yale - Economic Growth Center.
  8. Edward L. Glaeser & Jose A. Scheinkman, 2001. "Non-Market Interactions," Harvard Institute of Economic Research Working Papers 1914, Harvard - Institute of Economic Research.
  9. Chang, Sheng-Kai, 2007. "A simple asset pricing model with social interactions and heterogeneous beliefs," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1300-1325, April.
  10. Follmer, Hans & Horst, Ulrich & Kirman, Alan, 2005. "Equilibria in financial markets with heterogeneous agents: a probabilistic perspective," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 123-155, February.
  11. repec:att:wimass:9621 is not listed on IDEAS
  12. Paolo Dai Pra & Wolfgang J. Runggaldier & Elena Sartori & Marco Tolotti, 2007. "Large portfolio losses: A dynamic contagion model," Papers 0704.1348, arXiv.org, revised Mar 2009.
  13. Edward L. Glaeser & Jose A. Scheinkman, 1999. "Measuring Social Interactions," Harvard Institute of Economic Research Working Papers 1878, Harvard - Institute of Economic Research.
  14. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
  15. Blume,L. & Durlauf,S., 2002. "Equilibrium concepts for social interaction models," Working papers 7, Wisconsin Madison - Social Systems.
  16. Brock,W.A. & Durlauf,S.N., 2000. "Discrete choice with social interactions," Working papers 7, Wisconsin Madison - Social Systems.
  17. Cooper, Russell & John, Andrew, 1988. "Coordinating Coordination Failures in Keynesian Models," The Quarterly Journal of Economics, MIT Press, vol. 103(3), pages 441-63, August.
  18. Giesecke, Kay & Weber, Stefan, 2004. "Cyclical correlations, credit contagion, and portfolio losses," Journal of Banking & Finance, Elsevier, vol. 28(12), pages 3009-3036, December.
  19. Rüdiger Frey & Jochen Backhaus, 2008. "Pricing And Hedging Of Portfolio Credit Derivatives With Interacting Default Intensities," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(06), pages 611-634.
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Cited by:
  1. Emilio Barucci & Marco Tolotti, 2010. "Identity, reputation and social interaction with an application to sequential voting," Working Papers 204, Department of Applied Mathematics, Università Ca' Foscari Venezia.

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