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Dynamic Price Competition with Network Effects

  • Luís Cabral

    ()

    (New York University)

I consider a dynamic model of competition between two proprietary networks. Consumers die with a constant hazard rate and are replaced by new consumers. Firms compete for new consumers to join their network by offering network entry prices (which may be below cost). New consumers have a privately known preference for each network. Upon joining a network, in each period consumers enjoy a benefit which is increasing in network size during that period. Firms receive revenues from new consumers as well as from consumers already belonging to their network. I discuss various properties of the equilibrium, including the pricing function, the system’s expected motion, and the stationary distribution of market shares. I derive several results analytically. I then confirm and extend these results by numerical computation. Finally, I use the model to estimate the barrier to entry create by network effects.

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File URL: http://www.concorrencia.pt/download/WP22_networksApr07.pdf
File Function: First version, 2007
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Paper provided by Portuguese Competition Authority in its series Working Papers with number 22.

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Length: 34 pages
Date of creation: Apr 2007
Date of revision:
Handle: RePEc:pca:wpaper:22
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  1. Farrell, Joseph & Klemperer, Paul, 2007. "Coordination and Lock-In: Competition with Switching Costs and Network Effects," Handbook of Industrial Organization, Elsevier.
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  4. Beggs, Alan & Klemperer, Paul, 1990. "Multi-Period Competition with Switching Costs," CEPR Discussion Papers 436, C.E.P.R. Discussion Papers.
  5. Andrew Caplin & Barry Nalebuff, 1990. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Cowles Foundation Discussion Papers 937, Cowles Foundation for Research in Economics, Yale University.
  6. Cabral, Luis M B & Riordan, Michael H, 1994. "The Learning Curve, Market Dominance, and Predatory Pricing," Econometrica, Econometric Society, vol. 62(5), pages 1115-40, September.
  7. Cantillon, Estelle & Yin, Pai-Ling, 2007. "How and when do markets tip? Lessons from the Battle of the Bund," Working Paper Series 0766, European Central Bank.
  8. Jean-Jacques Laffont & Patrick Rey & Jean Tirole, 1998. "Network Competition: II. Price Discrimination," RAND Journal of Economics, The RAND Corporation, vol. 29(1), pages 38-56, Spring.
  9. Matthew Mitchell & Andrzej Skrzypacz, 2006. "Network externalities and long-run market shares," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(3), pages 621-648, November.
  10. Katz, Michael L & Shapiro, Carl, 1985. "Network Externalities, Competition, and Compatibility," American Economic Review, American Economic Association, vol. 75(3), pages 424-40, June.
  11. Nicholas Economides, 1995. "The Economics of Networks," Working Papers 94-24, New York University, Leonard N. Stern School of Business, Department of Economics, revised Sep 1995.
  12. Luís M. B. Cabral & Miguel Villas-Boas, 2005. "Bertrand Supertraps," Management Science, INFORMS, vol. 51(4), pages 599-613, April.
  13. Arthur, W Brian, 1989. "Competing Technologies, Increasing Returns, and Lock-In by Historical Events," Economic Journal, Royal Economic Society, vol. 99(394), pages 116-31, March.
  14. Jullien, Bruno, 2000. "Competing in Network Industries: Divide and Conquer," IDEI Working Papers 112, Institut d'Économie Industrielle (IDEI), Toulouse, revised Jul 2001.
  15. Neil Gandal, 1994. "Hedonic Price Indexes for Spreadsheets and an Empirical Test for Network Externalities," RAND Journal of Economics, The RAND Corporation, vol. 25(1), pages 160-170, Spring.
  16. Jean-Jacques Laffont & Patrick Rey & Jean Tirole, 1998. "Network Competition: I. Overview and Nondiscriminatory Pricing," RAND Journal of Economics, The RAND Corporation, vol. 29(1), pages 1-37, Spring.
  17. Christopher Budd & Christopher Harris & John Vickers, 1993. "A Model of the Evolution of Duopoly: Does the Asymmetry between Firms Tend to Increase or Decrease?," Review of Economic Studies, Oxford University Press, vol. 60(3), pages 543-573.
  18. Marc Rysman, 2004. "Competition Between Networks: A Study of the Market for Yellow Pages," Review of Economic Studies, Oxford University Press, vol. 71(2), pages 483-512.
  19. Ulrich Doraszelski & Joe Harrington & Jiawei Chen, 2009. "Avoiding Market Dominance: Product Compatibility in Markets with Network Effects," 2009 Meeting Papers 30, Society for Economic Dynamics.
  20. Joseph Farrell & Garth Saloner, 1985. "Standardization, Compatibility, and Innovation," RAND Journal of Economics, The RAND Corporation, vol. 16(1), pages 70-83, Spring.
  21. Robin S. Lee, 2013. "Vertical Integration and Exclusivity in Platform and Two-Sided Markets," American Economic Review, American Economic Association, vol. 103(7), pages 2960-3000, December.
  22. Goolsbee, Austan & Klenow, Peter J, 2002. "Evidence on Learning and Network Externalities in the Diffusion of Home Computers," Journal of Law and Economics, University of Chicago Press, vol. 45(2), pages 317-43, October.
  23. Luis Cabral, 2000. "Increasing Dominance With No Efficiency Effect," Working Papers 00-06, New York University, Leonard N. Stern School of Business, Department of Economics.
  24. Athey, Susan & Schmutzler, Armin, 2001. "Investment and Market Dominance," RAND Journal of Economics, The RAND Corporation, vol. 32(1), pages 1-26, Spring.
  25. Robin S. Lee, 2007. "Vertical Integration and Exclusivity in Two-Sided Markets," Working Papers 07-39, NET Institute, revised Aug 2012.
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