Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/hal/journl/halshs-04004539.html
   My bibliography  Save this paper

Discrete Choices under Social Influence, Generic Properties

Author

Listed:
  • Mirta Gordon

    (AMA - Analyse de données, Modélisation et Apprentissage automatique [Grenoble] - LIG - Laboratoire d'Informatique de Grenoble - UPMF - Université Pierre Mendès France - Grenoble 2 - UJF - Université Joseph Fourier - Grenoble 1 - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - INPG - Institut National Polytechnique de Grenoble - CNRS - Centre National de la Recherche Scientifique)

  • Jean-Pierre Nadal

    (CAMS - Centre d'Analyse et de Mathématique sociales - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique, LPS - Laboratoire de Physique Statistique de l'ENS - FRDPENS - Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

  • Denis Phan

    (GEMAS - Groupe d'étude des méthodes de l'analyse sociologique - UP4 - Université Paris-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Viktoriya Semeshenko

    (Departamento de Economía [Buenos Aires] - Facultad de Ciencias Económicas [Buenos Aires] - UBA - Universidad de Buenos Aires [Buenos Aires])

Abstract
We consider a model of socially interacting individuals that make a binary choice in a context of positive additive endogenous externalities. It encompasses as particular cases several models from the sociology and economics literature. We extend previous results to the case of a general distribution of idiosyncratic preferences, called here Idiosyncratic Willingnesses to Pay (IWP). When j, the ratio of the social influence strength to the standard deviation of the IWP distribution, is small enough, the inverse demand is a classical monotonic (decreasing) function of the adoption rate. However, even if the IWP distribution is mono-modal, there is a critical value of j above which the inverse demand is non-monotonic. Thus, depending on the price, there are either one or several equilibria. Beyond this first result, we exhibit the generic properties of the boundaries limiting the regions where the system presents different types of equilibria (unique or multiple). These properties are shown to depend only on qualitative features of the IWP distribution: modality (number of maxima), smoothness and type of support (compact or infinite). The main results are summarized as phase diagrams in the space of the model parameters, on which the regions of multiple equilibria are precisely delimited. We also discuss the links between the model and the random field Ising model studied in the physics literature.

Suggested Citation

  • Mirta Gordon & Jean-Pierre Nadal & Denis Phan & Viktoriya Semeshenko, 2012. "Discrete Choices under Social Influence, Generic Properties," Post-Print halshs-04004539, HAL.
    • Handle: RePEc:hal:journl:halshs-04004539
    DOI: 10.1142/S0218202509003887
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Jean-Philippe Bouchaud, 2000. "Power-laws in economics and finance: some ideas from physics," Science & Finance (CFM) working paper archive 500023, Science & Finance, Capital Fund Management.
    3. Krauth, Brian V., 2006. "Simulation-based estimation of peer effects," Journal of Econometrics, Elsevier, vol. 133(1), pages 243-271, July.
    4. Burckhard von Rabenau & Konrad Stahl, 1974. "Dynamic Aspects of Public Goods: A Further Analysis of the Telephone System," Bell Journal of Economics, The RAND Corporation, vol. 5(2), pages 651-669, Autumn.
    5. Weisbuch, Gerard & Kirman, Alan & Herreiner, Dorothea, 2000. "Market Organisation and Trading Relationships," Economic Journal, Royal Economic Society, vol. 110(463), pages 411-436, April.
    6. 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.
    7. 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.
    8. Yannis M. Ioannides & Jeffrey E. Zabel, 2003. "Neighbourhood effects and housing demand," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(5), pages 563-584.
    9. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    10. Blume,L.E. & Durlauf,S.N., 2005. "Identifying social interactions : a review," Working papers 12, Wisconsin Madison - Social Systems.
    11. Becker, Gary S, 1991. "A Note on Restaurant Pricing and Other Examples of Social Influences on Price," Journal of Political Economy, University of Chicago Press, vol. 99(5), pages 1109-1116, October.
    12. Quentin Michard & Jean-Philippe Bouchaud, 2005. "Theory of collective opinion shifts: from smooth trends to abrupt swings," Science & Finance (CFM) working paper archive 500060, Science & Finance, Capital Fund Management.
    13. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    14. Granovetter, Mark & Soong, Roland, 1986. "Threshold models of interpersonal effects in consumer demand," Journal of Economic Behavior & Organization, Elsevier, vol. 7(1), pages 83-99, March.
    15. Steven N. Durlauf, 1993. "Nonergodic Economic Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(2), pages 349-366.
    16. Charles F. Manski, 2000. "Economic Analysis of Social Interactions," Journal of Economic Perspectives, American Economic Association, vol. 14(3), pages 115-136, Summer.
    17. Richard Baldwin & Paul Krugman, 1989. "Persistent Trade Effects of Large Exchange Rate Shocks," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 104(4), pages 635-654.
    18. Bulow, Jeremy I & Geanakoplos, John D & Klemperer, Paul D, 1985. "Multimarket Oligopoly: Strategic Substitutes and Complements," Journal of Political Economy, University of Chicago Press, vol. 93(3), pages 488-511, June.
    19. Durlauf, Steven N, 1996. "A Theory of Persistent Income Inequality," Journal of Economic Growth, Springer, vol. 1(1), pages 75-93, March.
    20. Viktoriya Semeshenko & Mirta B. Gordon & Jean-Pierre Nadal & Denis Phan, 2006. "Choice under Social Influence: Effects of Learning Behaviours on the Collective Dynamics," Contributions to Economic Analysis, in: Cognitive Economics: New Trends, pages 177-203, Emerald Group Publishing Limited.
    21. Gordon, Mirta B. & Nadal, Jean-Pierre & Phan, Denis & Vannimenus, Jean, 2005. "Seller's dilemma due to social interactions between customers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 356(2), pages 628-640.
    22. Solomon, Sorin & Weisbuch, Gerard & de Arcangelis, Lucilla & Jan, Naeem & Stauffer, Dietrich, 2000. "Social percolation models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 277(1), pages 239-247.
    23. Brian Krauth, 2006. "Social interactions in small groups," Canadian Journal of Economics, Canadian Economics Association, vol. 39(2), pages 414-433, May.
    24. Bernheim, B Douglas, 1994. "A Theory of Conformity," Journal of Political Economy, University of Chicago Press, vol. 102(5), pages 841-877, October.
    25. S. N. Durlauf, "undated". "A Framework for the Study of Individual Behavior and Social Interactions," Institute for Research on Poverty Discussion Papers 1220-01, University of Wisconsin Institute for Research on Poverty.
    26. Daniel L. McFadden, 1976. "Quantal Choice Analysis: A Survey," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 363-390, National Bureau of Economic Research, Inc.
    27. Nicolas Curien & Michel Gensollen, 1987. "Les théories de la demande de raccordement téléphonique," Revue Économique, Programme National Persée, vol. 38(2), pages 203-256.
    28. 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.
    29. Michael L. Katz & Carl Shapiro, 1994. "Systems Competition and Network Effects," Journal of Economic Perspectives, American Economic Association, vol. 8(2), pages 93-115, Spring.
    30. Weisbuch, Gérard & Stauffer, Dietrich, 2003. "Adjustment and social choice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 323(C), pages 651-662.
    31. 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.
    32. Jeffrey Rohlfs, 1974. "A Theory of Interdependent Demand for a Communications Service," Bell Journal of Economics, The RAND Corporation, vol. 5(1), pages 16-37, Spring.
    33. Bouchaud,Jean-Philippe & Potters,Marc, 2003. "Theory of Financial Risk and Derivative Pricing," Cambridge Books, Cambridge University Press, number 9780521819169, October.
    34. Roland Bénabou, 1996. "Equity and Efficiency in Human Capital Investment: The Local Connection," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(2), pages 237-264.
    35. Q. Michard & J.-P. Bouchaud, 2005. "Theory of collective opinion shifts: from smooth trends to abrupt swings," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 47(1), pages 151-159, September.
    36. Denis Phan & Stephane Pajot & Jean-Pierre Nadal, 2003. "The Monopolist's Market with Discrete Choices and Network Externality Revisited: Small-Worlds, Phase Transition and Avalanches in an ACE Framework," Computing in Economics and Finance 2003 150, Society for Computational Economics.
    37. H. Leibenstein, 1950. "Bandwagon, Snob, and Veblen Effects in the Theory of Consumers' Demand," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 64(2), pages 183-207.
    38. Christian Borghesi & Jean-Philippe Bouchaud, 2006. "Of Songs and Men: a Model for Multiple Choice with Herding," Papers physics/0606224, arXiv.org.
    39. Roland Artle & Christian Averous, 1973. "The Telephone System as a Public Good: Static and Dynamic Aspects," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 89-100, Spring.
    Full references (including those not matched with items on IDEAS)

    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. Mirta B. Gordon & Jean-Pierre Nadal & Denis Phan & Viktoriya Semeshenko, 2012. "Entanglement between Demand and Supply in Markets with Bandwagon Goods," Papers 1209.1321, arXiv.org, revised Dec 2012.
    2. Brock,W.A. & Durlauf,S.N., 2005. "Social interactions and macroeconomics," Working papers 5, Wisconsin Madison - Social Systems.
    3. Blume,L.E. & Durlauf,S.N., 2005. "Identifying social interactions : a review," Working papers 12, Wisconsin Madison - Social Systems.
    4. Viktoriya Semeshenko & Alexis Garapin & Bernard Ruffieux & Mirta Gordon, 2010. "Information-driven coordination: experimental results with heterogeneous individuals," Theory and Decision, Springer, vol. 69(1), pages 119-142, July.
    5. Steven N. Durlauf & Yannis M. Ioannides, 2010. "Social Interactions," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 451-478, September.
    6. Adriaan R. Soetevent, 2006. "Empirics of the Identification of Social Interactions; An Evaluation of the Approaches and Their Results," Journal of Economic Surveys, Wiley Blackwell, vol. 20(2), pages 193-228, April.
    7. ÖZGÜR, Onur & BISIN, Alberto, 2011. "Dynamic Linear Economies with Social Interactions," Cahiers de recherche 04-2011, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    8. Brock, William A. & Durlauf, Steven N., 2007. "Identification of binary choice models with social interactions," Journal of Econometrics, Elsevier, vol. 140(1), pages 52-75, September.
    9. Jean-Philippe Bouchaud, 2012. "Crises and collective socio-economic phenomena: simple models and challenges," Papers 1209.0453, arXiv.org, revised Dec 2012.
    10. Katarzyna Ostasiewicz & Michal H. Tyc & Piotr Goliczewski & Piotr Magnuszewski & Andrzej Radosz & Jan Sendzimir, 2006. "Integrating economic and psychological insights in binary choice models with social interactions," Papers physics/0609170, arXiv.org.
    11. Tolciu, Andreia, 2008. "Is unemployment a consequence of social interactions? Seeking for a common research framework for economists and other social scientists," HWWI Research Papers 1-15, Hamburg Institute of International Economics (HWWI).
    12. Brock,W.A. & Durlauf,S.N., 2003. "Multinomial choice with social interactions," Working papers 1, Wisconsin Madison - Social Systems.
    13. 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).
    14. Semeshenko, Viktoriya & Gordon, Mirta B. & Nadal, Jean-Pierre, 2008. "Collective states in social systems with interacting learning agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(19), pages 4903-4916.
    15. Steven N. Durlauf, 1996. "Statistical Mechanics Approaches to Socioeconomic Behavior," NBER Technical Working Papers 0203, National Bureau of Economic Research, Inc.
    16. Edward L. Glaeser & Jose Scheinkman, 2000. "Non-Market Interactions," NBER Working Papers 8053, National Bureau of Economic Research, Inc.
    17. Horst, Ulrich, 2010. "Dynamic systems of social interactions," Journal of Economic Behavior & Organization, Elsevier, vol. 73(2), pages 158-170, February.
    18. 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.
    19. 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.
    20. Grodner, Andrew & Kniesner, Thomas J. & Bishop, John A., 2011. "Social Interactions in the Labor Market," Foundations and Trends(R) in Microeconomics, now publishers, vol. 6(4), pages 265-366, September.

    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:hal:journl:halshs-04004539. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.