A limit theorem for systems of social interactions
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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- Föllmer, Hans & Horst, Ulrich, 2001.
"Convergence of locally and globally interacting Markov chains,"
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- Stephen Morris, "undated". "Interaction Games: A Unified Analysis of Incomplete Information, Local Interaction and Random Matching," Penn CARESS Working Papers 1879bf5487d743edef7f32bb2, Penn Economics Department.
- 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.
- Stephen Morris, "undated". ""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.
- Horst, Ulrich & Scheinkman, Jose A., 2006. "Equilibria in systems of social interactions," Journal of Economic Theory, Elsevier, vol. 130(1), pages 44-77, September.
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- 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.
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- 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.