IDEAS home Printed from
   My bibliography  Save this paper

Monopoly Market with Externality: an Analysis with Statistical Physics and Agent Based Computational Economics


  • Jean-Pierre Nadal

    (LPS, Ecole Normale Sup\'erieure, Paris, France)

  • Denis Phan

    (ENST Bretagne and ICI-UBO, Brest, France)

  • Mirta B. Gordon

    (Leibniz, Grenoble, France)

  • Jean Vannimenus

    (LPS, Ecole Normale Sup\'erieure, Paris, France)


We explore the effects of social influence in a simple market model in which a large number of agents face a binary choice: 'to buy/not to buy' a single unit of a product at a price posted by a single seller (the monopoly case). We consider the case of 'positive externalities': an agent is more willing to buy if the other agents with whom he/she interacts make the same decision. We compare two special cases known in the economics literature as the Thurstone and the McFadden approaches. We show that they correspond to modeling the heterogenity in individual decision rules with, respectively, annealed and quenched disorder. More precisely the first case leads to a standard Ising model at finite temperature in a uniform external field, and the second case to a random field Ising model (RFIM) at zero temperature. Considering the optimisation of profit by the seller within the McFadden/RFIM model in the mean field limit, we exhibit a new first order phase transition: if the social influence is strong enough, there is a regime where, if the mean willingness to pay increases, or if the production costs decrease, the optimal solution for the seller jumps from one with a high price and a small number of buyers, to another one with a low price and a large number of buyers.

Suggested Citation

  • Jean-Pierre Nadal & Denis Phan & Mirta B. Gordon & Jean Vannimenus, 2003. "Monopoly Market with Externality: an Analysis with Statistical Physics and Agent Based Computational Economics," Papers cond-mat/0311096,
  • Handle: RePEc:arx:papers:cond-mat/0311096

    Download full text from publisher

    File URL:
    File Function: Latest version
    Download Restriction: no

    References listed on IDEAS

    1. 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.
    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. Orlean, Andre, 1995. "Bayesian interactions and collective dynamics of opinion: Herd behavior and mimetic contagion," Journal of Economic Behavior & Organization, Elsevier, vol. 28(2), pages 257-274, October.
    4. Alan Kirman, 1997. "The economy as an evolving network," Journal of Evolutionary Economics, Springer, vol. 7(4), pages 339-353.
    5. 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.
    6. Weisbuch, GĂ©rard & Stauffer, Dietrich, 2003. "Adjustment and social choice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 323(C), pages 651-662.
    Full references (including those not matched with items on IDEAS)

    More about this item


    Access and download statistics


    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:arx:papers:cond-mat/0311096. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.