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Dynamic Systems of Social Interactions

  • Ulrich Horst

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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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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  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.
  2. 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.
  3. Yannis Ioannides, 2006. "Topologies of social interactions," Economic Theory, Springer, vol. 28(3), pages 559-584, 08.
  4. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  5. Brock, William A & Durlauf, Steven N, 2001. "Discrete Choice with Social Interactions," Review of Economic Studies, Wiley Blackwell, vol. 68(2), pages 235-60, April.
  6. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  7. Blume Lawrence E., 1995. "The Statistical Mechanics of Best-Response Strategy Revision," Games and Economic Behavior, Elsevier, vol. 11(2), pages 111-145, November.
  8. Horst, Ulrich, 2007. "Stochastic cascades, credit contagion, and large portfolio losses," Journal of Economic Behavior & Organization, Elsevier, vol. 63(1), pages 25-54, May.
  9. Yannis M. Ioannides & Adriaan R. Soetevent, 2005. "Social Networking and Individual Outcomes Beyond the Mean Field Case," Discussion Papers Series, Department of Economics, Tufts University 0521, Department of Economics, Tufts University.
  10. 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.
  11. Benaim, Michel & Weibull, Jörgen W., 2000. "Deterministic Approximation of Stochastic Evolution in Games," Working Paper Series 534, Research Institute of Industrial Economics, revised 30 Oct 2001.
  12. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
  13. Vives, X., 1988. "Nash Equilibrium With Strategic Complementarities," UFAE and IAE Working Papers 107-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  14. Topa, Giorgio, 1997. "Social Interactions, Local Spillovers and Unemployment," Working Papers 97-17, C.V. Starr Center for Applied Economics, New York University.
  15. 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.
  16. Follmer, Hans, 1974. "Random economies with many interacting agents," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 51-62, March.
  17. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
  18. 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.
  19. 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.
  20. U. Horst & Jose A. Scheinkman, 2010. "Equilibria in Systems of Social Interactions," Levine's Working Paper Archive 506439000000000119, David K. Levine.
  21. Michael Kosfeld, 2002. "Stochastic strategy adjustment in coordination games," Economic Theory, Springer, vol. 20(2), pages 321-339.
  22. 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.
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