IDEAS home Printed from https://ideas.repec.org/p/hum/wpaper/sfb649dp2010-012.html
   My bibliography  Save this paper

Dynamic Systems of Social Interactions

Author

Listed:
  • 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.

Suggested Citation

  • Ulrich Horst, 2010. "Dynamic Systems of Social Interactions," SFB 649 Discussion Papers SFB649DP2010-012, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2010-012
    as

    Download full text from publisher

    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2010-012.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Blume Lawrence E., 1995. "The Statistical Mechanics of Best-Response Strategy Revision," Games and Economic Behavior, Elsevier, vol. 11(2), pages 111-145, November.
    3. 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.
    4. Glenn Ellison, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(1), pages 17-45.
    5. Horst, Ulrich & Scheinkman, Jose A., 2006. "Equilibria in systems of social interactions," Journal of Economic Theory, Elsevier, vol. 130(1), pages 44-77, September.
    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. Yannis Ioannides, 2006. "Topologies of social interactions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(3), pages 559-584, August.
    8. William A. Brock & Steven N. Durlauf, 2001. "Discrete Choice with Social Interactions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(2), pages 235-260.
    9. Franklin Allen & Douglas Gale, 2000. "Financial Contagion," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 1-33, February.
    10. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    11. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    12. Michel BenaÔm & J–rgen W. Weibull, 2003. "Deterministic Approximation of Stochastic Evolution in Games," Econometrica, Econometric Society, vol. 71(3), pages 873-903, May.
    13. Steven N. Durlauf, 1993. "Nonergodic Economic Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(2), pages 349-366.
    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. Tesfatsion, Leigh & Judd, Kenneth L., 2006. "Handbook of Computational Economics, Vol. 2: Agent-Based Computational Economics," Staff General Research Papers Archive 10368, Iowa State University, Department of Economics.
    16. Michael Kosfeld, 2002. "Stochastic strategy adjustment in coordination games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(2), pages 321-339.
    17. Kosfeld, Michael, 2005. "Rumours and markets," Journal of Mathematical Economics, Elsevier, vol. 41(6), pages 646-664, September.
    18. Follmer, Hans, 1974. "Random economies with many interacting agents," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 51-62, March.
    19. 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.
    20. Giorgio Topa, 2001. "Social Interactions, Local Spillovers and Unemployment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(2), pages 261-295.
    21. 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.
    22. Föllmer, Hans & Horst, Ulrich, 2001. "Convergence of locally and globally interacting Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 96(1), pages 99-121, November.
    23. 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.
    24. 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.
    25. Leigh Tesfatsion & Kenneth L. Judd (ed.), 2006. "Handbook of Computational Economics," Handbook of Computational Economics, Elsevier, edition 1, volume 2, number 2.
    26. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    27. Ulrich Horst, 2005. "Financial price fluctuations in a stock market model with many interacting agents," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(4), pages 917-932, June.
    28. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nwaibeh, E.A. & Chikwendu, C.R., 2023. "A deterministic model of the spread of scam rumor and its numerical simulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 111-129.
    2. 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.
    3. Li, Ming & Zhang, Hong & Georgescu, Paul & Li, Tan, 2021. "The stochastic evolution of a rumor spreading model with two distinct spread inhibiting and attitude adjusting mechanisms in a homogeneous social network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 562(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Blume,L.E. & Durlauf,S.N., 2005. "Identifying social interactions : a review," Working papers 12, Wisconsin Madison - Social Systems.
    2. Evstigneev, Igor & Taksar, Michael, 2009. "Dynamic interaction models of economic equilibrium," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 166-182, January.
    3. La Ferrara, Eliana & Gulesci, Selim & Jindani, Sam & Smerdon, David & Sulaiman, Munshi & Young, H. Peyton, 2021. "A Stepping Stone Approach to Understanding Harmful Norms," CEPR Discussion Papers 15776, C.E.P.R. Discussion Papers.
    4. Opolot, Daniel & Azomahou, Theophile, 2012. "Learning and convergence in networks," MERIT Working Papers 2012-074, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    5. Schipper, Burkhard C., 2009. "Imitators and optimizers in Cournot oligopoly," Journal of Economic Dynamics and Control, Elsevier, vol. 33(12), pages 1981-1990, December.
    6. Horst, Ulrich & Scheinkman, Jose A., 2006. "Equilibria in systems of social interactions," Journal of Economic Theory, Elsevier, vol. 130(1), pages 44-77, September.
    7. Denis Phan, 2006. "Discrete Choices under Social Influence:Generic Properties," Post-Print halshs-00105857, HAL.
    8. 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.
    9. Choudhary, M. Ali & Michael Orszag, J., 2008. "A cobweb model with local externalities," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 821-847, March.
    10. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications,, Elsevier.
    11. Russell Golman, 2011. "Why learning doesn’t add up: equilibrium selection with a composition of learning rules," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 719-733, November.
    12. Hofbauer, Josef & Sandholm, William H., 2007. "Evolution in games with randomly disturbed payoffs," Journal of Economic Theory, Elsevier, vol. 132(1), pages 47-69, January.
    13. Brock,W.A. & Durlauf,S.N., 2005. "Social interactions and macroeconomics," Working papers 5, Wisconsin Madison - Social Systems.
    14. H Peyton Young, 2014. "The Evolution of Social Norms," Economics Series Working Papers 726, University of Oxford, Department of Economics.
    15. Steven N. Durlauf & Yannis M. Ioannides, 2010. "Social Interactions," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 451-478, September.
    16. Kreindler, Gabriel E. & Young, H. Peyton, 2013. "Fast convergence in evolutionary equilibrium selection," Games and Economic Behavior, Elsevier, vol. 80(C), pages 39-67.
    17. Kosfeld, Michael, 2002. "Why shops close again: An evolutionary perspective on the deregulation of shopping hours," European Economic Review, Elsevier, vol. 46(1), pages 51-72, January.
    18. Azomahou, T. & Opolot, D., 2014. "Stability and strategic diffusion in networks," MERIT Working Papers 2014-035, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    19. Alós-Ferrer, Carlos & Weidenholzer, Simon, 2008. "Contagion and efficiency," Journal of Economic Theory, Elsevier, vol. 143(1), pages 251-274, November.
    20. Hsiao-Chi Chen & Yunshyong Chow & Li-Chau Wu, 2013. "Imitation, local interaction, and coordination," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 1041-1057, November.

    More about this item

    Keywords

    evolutionary dynamics; social interaction; equilibrium; interacting particle systems; coordination games;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hum:wpaper:sfb649dp2010-012. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: RDC-Team (email available below). General contact details of provider: https://edirc.repec.org/data/sohubde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.