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A limit theorem for systems of social interactions

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  • Horst, Ulrich
  • Scheinkman, José A.

Abstract

In this paper, we establish a convergence result for equilibria in systems of social interactions with many locally and globally interacting players. Assuming spacial homogeneity and that interactions between different agents are not too strong, we show that equilibria of systems with finitely many players converge to the unique equilibrium of a benchmark system with infinitely many agents. We prove convergence of individual actions and of average behavior. Our results also apply to a class of interaction games.

Suggested Citation

  • Horst, Ulrich & Scheinkman, José A., 2009. "A limit theorem for systems of social interactions," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 609-623, September.
  • Handle: RePEc:eee:mateco:v:45:y:2009:i:9-10:p:609-623
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    References listed on IDEAS

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    1. Föllmer, Hans & Horst, Ulrich, 2001. "Convergence of locally and globally interacting Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 96(1), pages 99-121, November.
    2. Stephen Morris, "undated". "Interaction Games: A Unified Analysis of Incomplete Information, Local Interaction and Random Matching," Penn CARESS Working Papers 1879bf5487d743edef7f32bb2, Penn Economics Department.
    3. Horst, Ulrich & Scheinkman, Jose A., 2006. "Equilibria in systems of social interactions," Journal of Economic Theory, Elsevier, vol. 130(1), pages 44-77, September.
    4. Edward L. Glaeser & Jose Scheinkman, 2000. "Non-Market Interactions," NBER Working Papers 8053, National Bureau of Economic Research, Inc.
    5. William A. Brock & Steven N. Durlauf, 2001. "Discrete Choice with Social Interactions," Review of Economic Studies, Oxford University Press, vol. 68(2), pages 235-260.
    6. Stephen Morris & Hyun Song Shin, 2003. "Heterogeneity and Uniqueness in Interaction Games," Cowles Foundation Discussion Papers 1402, Cowles Foundation for Research in Economics, Yale University.
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    Cited by:

    1. Horst, Ulrich & Scheinkman, Jose A., 2006. "Equilibria in systems of social interactions," Journal of Economic Theory, Elsevier, vol. 130(1), pages 44-77, September.
    2. Sun, Ruoyan, 2013. "Kinetics of jobs in multi-link cities with migration-driven aggregation process," Economic Modelling, Elsevier, vol. 30(C), pages 36-41.
    3. Alberto Bisin & Thierry Verdier, 2010. "The Economics of Cultural Transmission and Socialization," NBER Working Papers 16512, National Bureau of Economic Research, Inc.
    4. Fu, Guanxing & Horst, Ulrich, 2017. "Mean Field Games with Singular Controls," Rationality and Competition Discussion Paper Series 22, CRC TRR 190 Rationality and Competition.

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