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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. Follmer, Hans, 1974. "Random economies with many interacting agents," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 51-62, March.
  2. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  3. Yannis M. Ioannides, 2004. "Topologies Of Social Interactions," Econometric Society 2004 North American Winter Meetings 287, Econometric Society.
  4. 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.
  5. L. Blume, 2010. "The Statistical Mechanics of Strategic Interaction," Levine's Working Paper Archive 488, David K. Levine.
  6. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  7. Cars H. Hommes, 2005. "Heterogeneous Agent Models in Economics and Finance," Tinbergen Institute Discussion Papers 05-056/1, Tinbergen Institute.
  8. 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.
  9. Lawrence Blume, 1993. "The Statistical Mechanics of Best-Response Strategy Revision," Game Theory and Information 9307001, EconWPA, revised 26 Jan 1994.
  10. 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.
  11. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  12. Michael Kosfeld, 2002. "Stochastic strategy adjustment in coordination games," Economic Theory, Springer, vol. 20(2), pages 321-339.
  13. 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.
  14. 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.
  15. U. Horst & Jose A. Scheinkman, 2010. "Equilibria in Systems of Social Interactions," Levine's Working Paper Archive 506439000000000119, David K. Levine.
  16. repec:wop:humbsf:2001-29 is not listed on IDEAS
  17. Brock,W.A. & Durlauf,S.N., 2000. "Discrete choice with social interactions," Working papers 7, Wisconsin Madison - Social Systems.
  18. Topa, Giorgio, 2001. "Social Interactions, Local Spillovers and Unemployment," Review of Economic Studies, Wiley Blackwell, vol. 68(2), pages 261-95, April.
  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. Horst, Ulrich, 2007. "Stochastic cascades, credit contagion, and large portfolio losses," Journal of Economic Behavior & Organization, Elsevier, vol. 63(1), pages 25-54, May.
  21. repec:wop:humbsf:2001-21 is not listed on IDEAS
  22. Ulrich Horst, 2005. "Financial price fluctuations in a stock market model with many interacting agents," Economic Theory, Springer, vol. 25(4), pages 917-932, 06.
  23. 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.
  24. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
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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, vol. 82(2), pages 479-493.

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