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A limit theorem for systems of social interactions

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Author Info

  • 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.

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File URL: http://www.sciencedirect.com/science/article/B6VBY-4RDS1WB-2/2/0c8213b024e5ad60cc1b7384cbf8c52c
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Bibliographic Info

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

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Web page: http://www.elsevier.com/locate/jmateco

Related research

Keywords: Convergence of equilibria Global interactions Local interactions Random interaction structure;

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References

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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  1. Edward L. Glaeser & Jose A. Scheinkman, 2001. "Non-Market Interactions," Harvard Institute of Economic Research Working Papers 1914, Harvard - Institute of Economic Research.
  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. Brock,W.A. & Durlauf,S.N., 2000. "Discrete choice with social interactions," Working papers 7, Wisconsin Madison - Social Systems.
  4. 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.
  5. Stephen Morris, . ""Interaction Games: A Unified Analysis of Incomplete Information, Local Interaction and Random Matching''," CARESS Working Papres 97-02, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  6. repec:wop:humbsf:2001-21 is not listed on IDEAS
  7. 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.
  8. repec:wop:humbsf:2001-29 is not listed on IDEAS
  9. 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.
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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.

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