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Dynamic Systems of Social Interactions

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  • Ulrich Horst

Abstract

We state conditions for existence and uniqueness of equilibria in evolu- tionary models with an infinity of locally and globally interacting agents. Agents face repeated discrete choice problems. Their utility depends on the actions of some designated neighbors and the average choice throughout the whole population. We show that the dynamics on the level of aggregate be- havior can be described by a deterministic measure-valued integral equation. If some form of positive complementarities prevails we establish convergence and ergodicity results for aggregate activities. We apply our convergence re- sults to study a class of population games with random matching.

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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2010-012.

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Length: 24 pages
Date of creation: Feb 2010
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2010-012

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Keywords: evolutionary dynamics; social interaction; equilibrium; interacting particle systems; coordination games;

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References

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  1. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers, Princeton, Woodrow Wilson School - John M. Olin Program 71, Princeton, Woodrow Wilson School - John M. Olin Program.
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  6. Föllmer, Hans & Horst, Ulrich, 2001. "Convergence of locally and globally interacting Markov chains," SFB 373 Discussion Papers, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 2001,21, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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  13. Vives, X., 1988. "Nash Equilibrium With Strategic Complementarities," UFAE and IAE Working Papers, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) 107-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
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  15. Bisin, Alberto & Horst, Ulrich & Ozgur, Onur, 2006. "Rational expectations equilibria of economies with local interactions," Journal of Economic Theory, Elsevier, Elsevier, vol. 127(1), pages 74-116, March.
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  19. Ulrich Horst, 2005. "Financial price fluctuations in a stock market model with many interacting agents," Economic Theory, Springer, Springer, vol. 25(4), pages 917-932, 06.
  20. J. Scheinkman & U. Horst, 2003. "Equilibria in Systems of Social Interactions," Princeton Economic Theory Working Papers, David K. Levine d5a39039d26e0b08775b915bf, David K. Levine.
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Cited by:
  1. Grajzl, Peter & Baniak, Andrzej, 2012. "Mandating behavioral conformity in social groups with conformist members," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 82(2), pages 479-493.

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