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Multiple equilibria in a monopoly market with heterogeneous agents and externalities

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  • Jean-Pierre Nadal
  • Denis Phan
  • Mirta Gordon
  • Jean Vannimenus

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 (monopoly market). We consider the case of positive externalities: an agent is more willing to buy if other agents make the same decision. We consider two special cases of heterogeneity in the individuals' decision rules, corresponding in the literature to the Random Utility Models of Thurstone, and of McFadden and Manski. In the first one the heterogeneity fluctuates with time, leading to a standard model in Physics: the Ising model at finite temperature (known as annealed disorder) in a uniform external field. In the second approach the heterogeneity among agents is fixed; in Physics this is a particular case of the quenched disorder model known as a random field Ising model, at zero temperature. We study analytically the equilibrium properties of the market in the limiting case where each agent is influenced by all the others (the mean field limit), and we illustrate some dynamic properties of these models making use of numerical simulations in an Agent based Computational Economics approach. Considering the optimization of the profit by the seller within the case of fixed heterogeneity with global externality, we exhibit a new regime where, if the mean willingness to pay increases and/or the production costs decrease, the seller's optimal strategy jumps from a solution with a high price and a small number of buyers, to another one with a low price and a large number of buyers. This regime, usually modelled with ad hoc bimodal distributions of the idiosyncratic heterogeneity, arises here for general monomodal distributions if the social influence is strong enough.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

Volume (Year): 5 (2005)
Issue (Month): 6 ()
Pages: 557-568

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Handle: RePEc:taf:quantf:v:5:y:2005:i:6:p:557-568

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References

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  1. Jeremy I. Bulow & John Geanakoplos & Paul D. Klemperer, 1983. "Multimarket Oligopoly," Cowles Foundation Discussion Papers 674, Cowles Foundation for Research in Economics, Yale University.
  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. 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.
  4. Bulow, Jeremy I & Geanakoplos, John D & Klemperer, Paul D, 1985. "Multimarket Oligopoly: Strategic Substitutes and Complements," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 93(3), pages 488-511, June.
  5. Weisbuch, Gérard & Stauffer, Dietrich, 2003. "Adjustment and social choice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 323(C), pages 651-662.
  6. 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.
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Cited by:
  1. Y. P. Ma & S. Gonçalves & S. Mignot & J.-P. Nadal & M. B. Gordon, 2009. "Cycles of cooperation and free-riding in social systems," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 71(4), pages 597-610, October.
  2. 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.
  3. Paolo Dai Pra & Fulvio Fontini & Elena Sartori & Marco Tolotti, 2011. "Endogenous equilibria in liquid markets with frictions and boundedly rational agents," Working Papers 7, Department of Management, Università Ca' Foscari Venezia.
  4. Christian Borghesi & Jean-Philippe Bouchaud, 2007. "Of songs and men: a model for multiple choice with herding," Quality & Quantity: International Journal of Methodology, Springer, vol. 41(4), pages 557-568, August.
  5. Pigeard de Almeida Prado, Fernando & Belitsky, Vladimir & Ferreira, Alex Luiz, 2011. "Social interactions, product differentiation and discontinuity of demand," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 642-653.
  6. D. Sornette, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models," Papers 1404.0243, arXiv.org.
  7. Vincenzo Atella & Jay Bhattacharya & Lorenzo Carbonari, 2008. "Pharmaceutical Industry, Drug Quality and Regulation: Evidence from US and Italy," NBER Working Papers 14567, National Bureau of Economic Research, Inc.
  8. Kindler, A. & Solomon, S. & Stauffer, D., 2013. "Peer-to-peer and mass communication effect on opinion shifts," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 785-796.
  9. Schütz, Gunter M. & de Almeida Prado, Fernando Pigeard & Harris, Rosemary J. & Belitsky, Vladimir, 2009. "Short-time behaviour of demand and price viewed through an exactly solvable model for heterogeneous interacting market agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4126-4144.
  10. Vladimir Belitsky & Antonio L. Pereira & Fernando P. de Almeida Prado, 2009. "Stability analysis with applications of a two-dimensional dynamical system arising from a stochastic model of an asset market," Papers 0909.4815, arXiv.org.
  11. Gunter M. Sch\"utz & Fernando Pigeard de Almeida Prado & Rosemary J. Harris & Vladimir Belitsky, 2007. "Short-time behaviour of demand and price viewed through an exactly solvable model for heterogeneous interacting market agents," Papers 0801.0003, arXiv.org, revised Jun 2009.
  12. 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.
  13. 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.
  14. Paolo Pellizzari & Elena Sartori & Marco Tolotti, 2014. "Trade-in programs in the context of technological innovation with herding," Working Papers 4, Department of Management, Università Ca' Foscari Venezia.
  15. Jean-Philippe Bouchaud, 2012. "Crises and collective socio-economic phenomena: simple models and challenges," Papers 1209.0453, arXiv.org, revised Dec 2012.
  16. Sebastian Goncalves & M. F. Laguna & J. R. Iglesias, 2012. "Why, when, and how fast innovations are adopted," Papers 1208.2589, arXiv.org.
  17. G\'erard Weisbuch & Vincent Buskens & Luat Vuong, 2007. "Heterogeneity and Increasing Returns May Drive Socio-Economic Transitions," Papers 0706.1454, arXiv.org.

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