Dynamic Price Competition with Network Effects

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Dynamic Price Competition with Network Effects

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Luís Cabral () (New York University)

Additional information is available for the following registered author(s):

Luis M B Cabral

Abstract

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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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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Paper
- Cabral, Luís M B, 2008. "Dynamic Price Competition with Network Effects," CEPR Discussion Papers 6687, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
- Luis Cabral, 2008. "Dynamic Price Competition with Network Effects," Working Papers 08-4, New York University, Leonard N. Stern School of Business, Department of Economics. [Downloadable!]

This paper has been announced in the following NEP Reports:

NEP-ALL-2007-06-11 (All new papers)
NEP-COM-2007-06-11 (Industrial Competition)
NEP-CSE-2007-06-11 (Economics of Strategic Management)
NEP-MIC-2007-06-11 (Microeconomics)
NEP-NET-2007-06-11 (Network Economics)
NEP-TID-2007-06-11 (Technology & Industrial Dynamics)

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

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. [Downloadable!] (restricted)
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Goolsbee, Austan & Klenow, Peter J, 2002. "Evidence on Learning and Network Externalities in the Diffusion of Home Computers," Journal of Law & Economics, University of Chicago Press, vol. 45(2), pages 317-43, October.
Other versions:
- 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. [Downloadable!] (restricted)
Joseph Farrell & Garth Saloner, 1985. "Standardization, Compatibility, and Innovation," RAND Journal of Economics, The RAND Corporation, vol. 16(1), pages 70-83, Spring. [Downloadable!] (restricted)
Other versions:
- Joseph Farrell & Garth Saloner, 1984. "Standardization, Compatibility and Innovation," Working papers 345, Massachusetts Institute of Technology (MIT), Department of Economics.
Budd, Christopher & Harris, Christopher & Vickers, John, 1993. "A Model of the Evolution of Duopoly: Does the Asymmetry between Firms Tend to Increase or Decrease?," Review of Economic Studies, Blackwell Publishing, vol. 60(3), pages 543-73, July. [Downloadable!] (restricted)
Matthew Mitchell & Andrzej Skrzypacz, 2006. "Network externalities and long-run market shares," Economic Theory, Springer, vol. 29(3), pages 621-648, November. [Downloadable!] (restricted)
Other versions:
- Skrzypacz, Andrzej & Mitchell, Matthew F., 2005. "Network Externalities and Long-Run Market Shares," Research Papers 1879, Stanford University, Graduate School of Business. [Downloadable!]
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. [Downloadable!] (restricted)
Emmanuelle Auriol & Michel Benaim, 2000. "Standardization in Decentralized Economies," American Economic Review, American Economic Association, vol. 90(3), pages 550-570, June. [Downloadable!] (restricted)
Other versions:
- AURIOL, Emmanuelle & BENAIM, Michel, 1999. "Standardization in Decentralized Economies," IDEI Working Papers 85, Institut d'Économie Industrielle (IDEI), Toulouse.
- Auriol, E. & Benaim, M., 1998. "Standardization in Decentralized Economies," G.R.E.Q.A.M. 98a30, Universite Aix-Marseille III.
Cabral, Luis M. B., 2002. "Increasing Dominance with No Efficiency Effect," Journal of Economic Theory, Elsevier, vol. 102(2), pages 471-479, February. [Downloadable!] (restricted)
Other versions:
- Cabral, L., 2000. "Increasing Dominance with No Efficiency Effect," New York University, Leonard N. Stern School Finance Department Working Paper Seires 00-06, New York University, Leonard N. Stern School of Business-.
- 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. [Downloadable!]
Farrell, Joseph & Klemperer, Paul, 2007. "Coordination and Lock-In: Competition with Switching Costs and Network Effects," Handbook of Industrial Organization, Elsevier. [Downloadable!] (restricted)
Other versions:
- Joseph Farrell & Paul Klemperer, 2006. "Co-ordination and Lock-in: Competition with Switching Costs and Network Effects," Economics Papers 2006-W07, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
- Farrell, Joseph & Klemperer, Paul, 2006. "Coordination and Lock-In: Competition with Switching Costs and Network Effects," CEPR Discussion Papers 5798, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January. [Downloadable!] (restricted)
Other versions:
- Andrew Caplin & Barry Nalebuff, 1990. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Cowles Foundation Discussion Papers 937, Cowles Foundation, Yale University. [Downloadable!]
- Caplin, A. & Nalebuff, B., 1989. "Aggregation And Imperfect Competition: On The Existence Of Equilibrium," Discussion Papers 1989_30, Columbia University, Department of Economics.
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. [Downloadable!] (restricted)
Other versions:
- Cabral, L. & Riordan, M., 1992. "The Learning Curve, Market Dominance and Predatory Pricing," Papers 39, Boston University - Industry Studies Programme.
- Luis M.B. Cabral & Michael Riordan, 1992. "The Learning Curve, Market Dominance and Predatory Pricing," Papers 0039, Boston University - Industry Studies Programme.
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. [Downloadable!] (restricted)
Katz, Michael L & Shapiro, Carl, 1985. "Network Externalities, Competition, and Compatibility," American Economic Review, American Economic Association, vol. 75(3), pages 424-40, June. [Downloadable!] (restricted)
Athey, Susan & Schmutzler, Armin, 2001. "Investment and Market Dominance," RAND Journal of Economics, The RAND Corporation, vol. 32(1), pages 1-26, Spring.
Economides, Nicholas, 1996. "The economics of networks," International Journal of Industrial Organization, Elsevier, vol. 14(6), pages 673-699, October. [Downloadable!] (restricted)
Other versions:
- Nicholas Economides, 1997. "The Economics of Networks," Industrial Organization 9701002, EconWPA. [Downloadable!]
- 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. [Downloadable!]
- Nicholas Economides, 1997. "The Economics of Networks," Brazilian Electronic Journal of Economics, Department of Economics, Universidade Federal de Pernambuco, vol. 1(0), December. [Downloadable!]
Beggs, Alan W & Klemperer, Paul, 1992. "Multi-period Competition with Switching Costs," Econometrica, Econometric Society, vol. 60(3), pages 651-66, May. [Downloadable!] (restricted)
Other versions:
- Beggs, Alan & Klemperer, Paul, 1990. "Multi-Period Competition with Switching Costs," CEPR Discussion Papers 436, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)

Full references

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Harbord, David & Pagnozzi, Marco, 2008. "On-Net/Off-Net Price Discrimination and 'Bill-and-Keep' vs. 'Cost-Based' Regulation of Mobile Termination Rates," MPRA Paper 14540, University Library of Munich, Germany. [Downloadable!]

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