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Dynamic Price Competition with Network Effects

  • Luis Cabral

I consider a dynamic model of competition between two proprietary networks. Consumers die and are replaced with a constant hazard rate. 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. Using a combination of analytical and numerical methods, I discuss various properties of the equilibrium. I show that very small or very large networks tend to price higher than networks of intermediate size. I also show that, around symmetric states, the gap between the large and the small network tends to widen (increasing dominance) whereas the opposite is true (reversion to the mean) around very asymmetric states.

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File URL: http://w4.stern.nyu.edu/emplibrary/networksJan08.pdf
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Paper provided by New York University, Leonard N. Stern School of Business, Department of Economics in its series Working Papers with number 08-4.

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Date of creation: 2008
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Handle: RePEc:ste:nystbu:08-4
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New York University, Leonard N. Stern School of Business, Department of Economics, 44 West 4th Street, New York, NY 10012-1126

Phone: (212) 998-0860
Fax: (212) 995-4218
Web page: http://w4.stern.nyu.edu/economics/

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  1. 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.
  2. 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.
  3. 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.
  4. Nicholas Economides, 1997. "The Economics of Networks," Industrial Organization 9701002, EconWPA.
  5. Paul Klemperer & Joseph Farrell, 2006. "Coordination and Lock-In: Competition with Switching Costs and Network Effects," Economics Series Working Papers 2006-W07, University of Oxford, Department of Economics.
  6. 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.
  7. Michihiro, Kandori & Rob, Rafael, 1998. "Bandwagon Effects and Long Run Technology Choice," Games and Economic Behavior, Elsevier, vol. 22(1), pages 30-60, January.
  8. Jullien, Bruno, 2000. "Competing in Network Industries: Divide and Conquer," IDEI Working Papers 112, Institut d'Économie Industrielle (IDEI), Toulouse, revised Jul 2001.
  9. Michel Benaim & Emmanuelle Auriol, 2000. "Standardization in Decentralized Economies," American Economic Review, American Economic Association, vol. 90(3), pages 550-570, June.
  10. 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.
  11. Katz, Michael L & Shapiro, Carl, 1985. "Network Externalities, Competition, and Compatibility," American Economic Review, American Economic Association, vol. 75(3), pages 424-40, June.
  12. 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.
  13. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January.
  14. Athey, Susan & Schmutzler, Armin, 2001. "Investment and Market Dominance," RAND Journal of Economics, The RAND Corporation, vol. 32(1), pages 1-26, Spring.
  15. Jiawei Chen & Ulrich Doraszelski & Joseph E. Harrington, Jr., 2008. "Avoiding Market Dominance: Product Compatibility in Markets with Network Effects," Economics Working Paper Archive 537, The Johns Hopkins University,Department of Economics.
  16. 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.
  17. 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.
  18. Joseph Farrell & Garth Saloner, 1985. "Standardization, Compatibility, and Innovation," RAND Journal of Economics, The RAND Corporation, vol. 16(1), pages 70-83, Spring.
  19. Beggs, Alan & Klemperer, Paul, 1990. "Multi-Period Competition with Switching Costs," CEPR Discussion Papers 436, C.E.P.R. Discussion Papers.
  20. 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.
  21. Robin S. Lee, 2007. "Vertical Integration and Exclusivity in Two-Sided Markets," Working Papers 07-39, NET Institute, revised Aug 2012.
  22. Austan Goolsbee & Peter J. Klenow, 1999. "Evidence on Learning and Network Externalities in the Diffusion of Home Computers," NBER Working Papers 7329, National Bureau of Economic Research, Inc.
  23. 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.
  24. Luís M. B. Cabral & Miguel Villas-Boas, 2005. "Bertrand Supertraps," Management Science, INFORMS, vol. 51(4), pages 599-613, April.
  25. 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.
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