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A limit theorem for systems of social interactions

  • Horst, Ulrich
  • Scheinkman, José A.

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.

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File URL: http://www.sciencedirect.com/science/article/B6VBY-4RDS1WB-2/2/0c8213b024e5ad60cc1b7384cbf8c52c
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Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 45 (2009)
Issue (Month): 9-10 (September)
Pages: 609-623

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Handle: RePEc:eee:mateco:v:45:y:2009:i:9-10:p:609-623
Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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  1. Edward L. Glaeser & Jose Scheinkman, 2000. "Non-Market Interactions," NBER Working Papers 8053, National Bureau of Economic Research, Inc.
  2. Horst, Ulrich & Scheinkman, Jose A., 2006. "Equilibria in systems of social interactions," Journal of Economic Theory, Elsevier, vol. 130(1), pages 44-77, September.
  3. Föllmer, Hans & Horst, Ulrich, 2001. "Convergence of locally and globally interacting Markov chains," SFB 373 Discussion Papers 2001,21, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  4. Brock, William A & Durlauf, Steven N, 2001. "Discrete Choice with Social Interactions," Review of Economic Studies, Wiley Blackwell, vol. 68(2), pages 235-60, April.
  5. 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.
  6. Stephen Morris, 1997. "Interaction Games: A Unified Analysis of Incomplete Information, Local Interaction, and Random Matching," Research in Economics 97-08-072e, Santa Fe Institute.
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