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Dynamic systems of social interactions

  • Horst, Ulrich

We state conditions for existence and uniqueness of equilibria in evolutionary 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 behavior 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 results to study a class of population games with random matching.

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Article provided by Elsevier in its journal Journal of Economic Behavior & Organization.

Volume (Year): 73 (2010)
Issue (Month): 2 (February)
Pages: 158-170

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Handle: RePEc:eee:jeborg:v:73:y:2010:i:2:p:158-170
Contact details of provider: Web page: http://www.elsevier.com/locate/jebo

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  1. 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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  5. 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.
  6. Horst, Ulrich, 2007. "Stochastic cascades, credit contagion, and large portfolio losses," Journal of Economic Behavior & Organization, Elsevier, vol. 63(1), pages 25-54, May.
  7. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  8. Kosfeld, M., 1998. "Rumours and Markets," Discussion Paper 1998-23, Tilburg University, Center for Economic Research.
  9. Ioannides, Yannis M. & Soetevent, Adriaan R., 2007. "Social networking and individual outcomes beyond the mean field case," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 369-390.
  10. Kurtz, Thomas G., 1978. "Strong approximation theorems for density dependent Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 6(3), pages 223-240, February.
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  12. Lawrence Blume, 1993. "The Statistical Mechanics of Best-Response Strategy Revision," Game Theory and Information 9307001, EconWPA, revised 26 Jan 1994.
  13. U. Horst & Jose A. Scheinkman, 2010. "Equilibria in Systems of Social Interactions," Levine's Working Paper Archive 506439000000000119, David K. Levine.
  14. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  15. Horst, Ulrich, 2001. "Financial price fluctuations in a stock market model with many interacting agents," SFB 373 Discussion Papers 2001,36, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  16. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186 Elsevier.
  17. Kosfeld, M., 1999. "Stochastic Strategy Adjustment in Coordination Games," Research Memorandum 775, Tilburg University, School of Economics and Management.
  18. Steven N. Durlauf, 1991. "Nonergodic Economic Growth," NBER Working Papers 3719, National Bureau of Economic Research, Inc.
  19. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  20. Follmer, Hans, 1974. "Random economies with many interacting agents," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 51-62, March.
  21. Bisin, Alberto & Horst, Ulrich & Ozgur, Onur, 2006. "Rational expectations equilibria of economies with local interactions," Journal of Economic Theory, Elsevier, vol. 127(1), pages 74-116, March.
  22. L. Blume, 2010. "The Statistical Mechanics of Strategic Interaction," Levine's Working Paper Archive 488, David K. Levine.
  23. Tanabe, Yasuo, 2006. "The propagation of chaos for interacting individuals in a large population," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 125-152, March.
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  25. Alan P. Kirman, 1992. "Whom or What Does the Representative Individual Represent?," Journal of Economic Perspectives, American Economic Association, vol. 6(2), pages 117-136, Spring.
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