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

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  • 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)

Abstract

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.

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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number cond-mat/0311096.

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Date of creation: Nov 2003
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Handle: RePEc:arx:papers:cond-mat/0311096

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  1. 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.
  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. 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.
  4. 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.
  5. Alan Kirman, 1997. "The economy as an evolving network," Journal of Evolutionary Economics, Springer, vol. 7(4), pages 339-353.
  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.
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