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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. 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. Horst, Ulrich, 2001. "Asymptotics of locally interacting Markov chains with global signals," SFB 373 Discussion Papers 2001,29, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    3. William A. Brock & Steven N. Durlauf, 2001. "Discrete Choice with Social Interactions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(2), pages 235-260.
    4. Stephen Morris, "undated". "Interaction Games: A Unified Analysis of Incomplete Information, Local Interaction and Random Matching," Penn CARESS Working Papers 1879bf5487d743edef7f32bb2, Penn Economics Department.
    5. 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.
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    1. Löwe, Matthias & Schubert, Kristina & Vermet, Franck, 2020. "Multi-group binary choice with social interaction and a random communication structure—A random graph approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    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. Fu, Guanxing & Horst, Ulrich, 2017. "Mean Field Games with Singular Controls," Rationality and Competition Discussion Paper Series 22, CRC TRR 190 Rationality and Competition.
    4. Alberto Bisin & Thierry Verdier, 2010. "The Economics of Cultural Transmission and Socialization," Post-Print halshs-00754788, HAL.
    5. Sun, Ruoyan, 2013. "Kinetics of jobs in multi-link cities with migration-driven aggregation process," Economic Modelling, Elsevier, vol. 30(C), pages 36-41.

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