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Equilibrium Concepts for Social Interaction Models

Author

Listed:
  • Lawrence Blume

    (Department of Economics, Cornell University, Uris Hall, Ithaca, NY 14853, USA)

  • Steven Durlauf

    (Department of Economics, University of Wisconsin, 7234 Social Science Building, 1180 Observatory Drive, Madison, WI 53706, USA)

Abstract

This paper describes the relationship between two different binary choice social interaction models. The Brock and Durlauf (2001) model is essentially a static Nash equilibrium model with random utility preferences. In the Blume (2003) model is a population game model similar to Blume (1993), Kandori, Mailath and Rob (1993) and Young (1993). We show that the equilibria of the Brock–Durlauf model are steady states of a differential equation which is a deterministic approximation of the sample-path behavior of Blume's model. Moreover, the limit distribution of this model clusters around a subset of the steady states when the population is large.

Suggested Citation

  • Lawrence Blume & Steven Durlauf, 2003. "Equilibrium Concepts for Social Interaction Models," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 193-209.
    • Handle: RePEc:wsi:igtrxx:v:05:y:2003:i:03:n:s021919890300101x
    DOI: 10.1142/S021919890300101X
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    References listed on IDEAS

    as
    1. Brock, William A. & Durlauf, Steven N., 2001. "Interactions-based models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 54, pages 3297-3380, Elsevier.
    2. Edward L. Glaeser & Bruce Sacerdote & José A. Scheinkman, 1996. "Crime and Social Interactions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 111(2), pages 507-548.
    3. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    4. repec:hhs:iuiwop:534 is not listed on IDEAS
    5. Binmore Kenneth G. & Samuelson Larry & Vaughan Richard, 1995. "Musical Chairs: Modeling Noisy Evolution," Games and Economic Behavior, Elsevier, vol. 11(1), pages 1-35, October.
    6. Binmore, K. & Samuelson, L. & Vaughan, R., 1993. "Musical Chairs: Modelling Noisy Evolution," Working papers 9324, Wisconsin Madison - Social Systems.
    7. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    8. 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.
    9. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Discrete choice models; Nash equilibrium; stochastic stability;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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