IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-01463925.html
   My bibliography  Save this paper

Dynamic price competition in aftermarkets with network effects

Author

Listed:
  • Didier Laussel

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Joana Resende

    (CORE - Center of Operation Research and Econometrics [Louvain] - UCL - Université Catholique de Louvain = Catholic University of Louvain, CETE - Universidade do Porto = University of Porto)

Abstract

This paper studies the dynamic price competition between two firms that sell horizontally differentiated durable goods and, subsequently, provide exclusive complementary goods and services to their customers. The paper analyzes how optimal pricing strategies are affected by the existence of network effects associated with the size of firms' consumer base. The interaction is thoroughly analyzed as a continuous time linear-quadratic differential game. We provide a necessary and sufficient condition for the existence of a unique duopoly equilibrium in affine strategies. When this condition holds, we show that optimal pricing strategies crucially depend on the nature of the network effects.

Suggested Citation

  • Didier Laussel & Joana Resende, 2014. "Dynamic price competition in aftermarkets with network effects," Post-Print hal-01463925, HAL.
    • Handle: RePEc:hal:journl:hal-01463925
    DOI: 10.1016/j.jmateco.2013.10.002
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Amir, Rabah & Lazzati, Natalia, 2011. "Network effects, market structure and industry performance," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2389-2419.
    2. Griva, Krina & Vettas, Nikolaos, 2011. "Price competition in a differentiated products duopoly under network effects," Information Economics and Policy, Elsevier, vol. 23(1), pages 85-97, March.
    3. Ulrich Doraszelski & Mark Satterthwaite, 2010. "Computable Markov‐perfect industry dynamics," RAND Journal of Economics, RAND Corporation, vol. 41(2), pages 215-243, June.
    4. Markovich, Sarit & Moenius, Johannes, 2009. "Winning while losing: Competition dynamics in the presence of indirect network effects," International Journal of Industrial Organization, Elsevier, vol. 27(3), pages 346-357, May.
    5. Laussel, Didier & de Montmarin, Maxime & Van Long, Ngo, 2004. "Dynamic duopoly with congestion effects," International Journal of Industrial Organization, Elsevier, vol. 22(5), pages 655-677, May.
    6. Grilo, Isabel & Shy, Oz & Thisse, Jacques-Francois, 2001. "Price competition when consumer behavior is characterized by conformity or vanity," Journal of Public Economics, Elsevier, vol. 80(3), pages 385-408, June.
    7. Hodaka Morita & Michael Waldman, 2004. "Durable Goods, Monopoly Maintenance, and Time Inconsistency," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 13(2), pages 273-302, June.
    8. Severin Borenstein & Jeffrey K. Mackie‐Mason & Janet S. Netz, 2000. "Exercising Market Power in Proprietary Aftermarkets," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 9(3), pages 157-188, June.
    9. Amir, Rabah, 1996. "Continuous Stochastic Games of Capital Accumulation with Convex Transitions," Games and Economic Behavior, Elsevier, vol. 15(2), pages 111-131, August.
    10. Richard Ericson & Ariel Pakes, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(1), pages 53-82.
    11. Luís Cabral, 2011. "Dynamic Price Competition with Network Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(1), pages 83-111.
    12. Léonard,Daniel & Long,Ngo van, 1992. "Optimal Control Theory and Static Optimization in Economics," Cambridge Books, Cambridge University Press, number 9780521331586, September.
    13. Jiawei Chen & Ulrich Doraszelski & Joseph E. Harrington, Jr., 2009. "Avoiding market dominance: product compatibility in markets with network effects," RAND Journal of Economics, RAND Corporation, vol. 40(3), pages 455-485, September.
    14. Joseph Farrell & Carl Shapiro, 1988. "Dynamic Competition with Switching Costs," RAND Journal of Economics, The RAND Corporation, vol. 19(1), pages 123-137, Spring.
    15. d'Aspremont, C & Gabszewicz, Jean Jaskold & Thisse, J-F, 1979. "On Hotelling's "Stability in Competition"," Econometrica, Econometric Society, vol. 47(5), pages 1145-1150, September.
    16. Markovich, Sarit, 2008. "Snowball: A dynamic oligopoly model with indirect network effects," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 909-938, March.
    17. Michael L. Katz & Carl Shapiro, 1994. "Systems Competition and Network Effects," Journal of Economic Perspectives, American Economic Association, vol. 8(2), pages 93-115, Spring.
    18. repec:bla:jemstr:v:2:y:1993:i:4:p:593-614:a is not listed on IDEAS
    19. Paul Klemperer, 1987. "Markets with Consumer Switching Costs," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(2), pages 375-394.
    20. Rossella Argenziano, 2008. "Differentiated networks: equilibrium and efficiency," RAND Journal of Economics, RAND Corporation, vol. 39(3), pages 747-769, September.
    21. Jeffrey Rohlfs, 1974. "A Theory of Interdependent Demand for a Communications Service," Bell Journal of Economics, The RAND Corporation, vol. 5(1), pages 16-37, Spring.
    22. AMIR, Rabah, 2001. "Stochastic games in economics: the lattice-theoretic approach," LIDAM Discussion Papers CORE 2001059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    23. Chen, Zhiqi & Ross, Thomas W, 1993. "Refusals to Deal, Price Discrimination, and Independent Service Organizations," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 2(4), pages 593-614, Winter.
    24. Katz, Michael L & Shapiro, Carl, 1985. "Network Externalities, Competition, and Compatibility," American Economic Review, American Economic Association, vol. 75(3), pages 424-440, June.
    25. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, September.
    26. Zhiqi Chen & Thomas Ross & W. Stanbury, 1998. "Refusals to Deal and Aftermarkets," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 13(1), pages 131-151, April.
    27. 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.
    28. Klemperer, Paul D, 1987. "Entry Deterrence in Markets with Consumer Switching Costs," Economic Journal, Royal Economic Society, vol. 97(388a), pages 99-117, Supplemen.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bruno Jullien & Alessandro Pavan & Marc Rysman, 2021. "Two-sided markets, pricing, and network effects," Post-Print hal-03828345, HAL.
    2. Laussel, Didier & Van Long, Ngo & Resende, Joana, 2015. "Network effects, aftermarkets and the Coase conjecture: A dynamic Markovian approach," International Journal of Industrial Organization, Elsevier, vol. 41(C), pages 84-96.
    3. Cabral, Luís, 2014. "Aftermarket power and foremarket competition," International Journal of Industrial Organization, Elsevier, vol. 35(C), pages 60-69.
    4. Adriana Gama & Rim Lahmandi-Ayed & Ana Elisa Pereira, 2020. "Entry and mergers in oligopoly with firm-specific network effects," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 1139-1164, November.
    5. Rabah Amir & Igor Evstigneev & Adriana Gama, 2021. "Oligopoly with network effects: firm-specific versus single network," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 1203-1230, April.
    6. Pekka Sääskilahti, 2016. "Buying Decision Coordination and Monopoly Pricing of Network Goods," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 25(2), pages 313-333, April.
    7. Dainis Zēgners & Tobias Kretschmer, 2017. "Competition with Aftermarket Power When Consumers Are Heterogeneous," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 26(1), pages 96-122, February.
    8. Svetlana Boyarchenko, 2020. "Super- and submodularity of stopping games with random observations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 983-1022, November.
    9. Gary Biglaiser & Jacques Crémer, 2020. "The Value of Incumbency When Platforms Face Heterogeneous Customers," Post-Print hal-03049041, HAL.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Laussel, Didier & Van Long, Ngo & Resende, Joana, 2015. "Network effects, aftermarkets and the Coase conjecture: A dynamic Markovian approach," International Journal of Industrial Organization, Elsevier, vol. 41(C), pages 84-96.
    2. Jullien, Bruno & Pavan, Alessandro & Rysman, Marc, 2021. "Two-sided Markets, Pricing, and Network Effects," TSE Working Papers 21-1238, Toulouse School of Economics (TSE).
    3. Suleymanova Irina & Wey Christian, 2011. "Bertrand Competition in Markets with Network Effects and Switching Costs," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 11(1), pages 1-58, September.
    4. Oz Shy, 2011. "A Short Survey of Network Economics," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 38(2), pages 119-149, March.
    5. Schneider, Lorenz, 2014. "Firm value in emerging network industries," Information Economics and Policy, Elsevier, vol. 26(C), pages 75-87.
    6. Griva, Krina & Vettas, Nikolaos, 2011. "Price competition in a differentiated products duopoly under network effects," Information Economics and Policy, Elsevier, vol. 23(1), pages 85-97, March.
    7. Alfredo Garcia & Yue Sun & Joseph Shen, 2014. "Dynamic Platform Competition with Malicious Users," Dynamic Games and Applications, Springer, vol. 4(3), pages 290-308, September.
    8. Navarro, Noemí, 2012. "Price and quality decisions under network effects," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 263-270.
    9. Jiawei Chen-super-†, 2016. "How Do Switching Costs Affect Market Concentration and Prices in Network Industries?," Journal of Industrial Economics, Wiley Blackwell, vol. 64(2), pages 226-254, June.
    10. Ngo Long, 2015. "Dynamic Games Between Firms and Infinitely Lived Consumers: A Review of the Literature," Dynamic Games and Applications, Springer, vol. 5(4), pages 467-492, December.
    11. Tingting He & Dmitri Kuksov & Chakravarthi Narasimhan, 2012. "Intraconnectivity and Interconnectivity: When Value Creation May Reduce Profits," Marketing Science, INFORMS, vol. 31(4), pages 587-602, July.
    12. Belleflamme,Paul & Peitz,Martin, 2015. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9781107687899.
    13. Mark J. Tremblay, 2019. "Platform Competition and Endogenous Switching Costs," Journal of Industry, Competition and Trade, Springer, vol. 19(4), pages 537-559, December.
    14. Chen, Jiawei, 2018. "Switching costs and network compatibility," International Journal of Industrial Organization, Elsevier, vol. 58(C), pages 1-30.
    15. Corrado Benassi & Marcella Scrimitore, 2017. "Income Distribution in Network Markets," Journal of Industry, Competition and Trade, Springer, vol. 17(3), pages 251-271, September.
    16. Pekka Sääskilahti, 2016. "Buying Decision Coordination and Monopoly Pricing of Network Goods," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 25(2), pages 313-333, April.
    17. Amir, Rabah & Lazzati, Natalia, 2011. "Network effects, market structure and industry performance," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2389-2419.
    18. Herings, P. Jean-Jacques & Peeters, Ronald & Yang, Michael S., 2018. "Piracy on the Internet: Accommodate it or fight it? A dynamic approach," European Journal of Operational Research, Elsevier, vol. 266(1), pages 328-339.
    19. Michael Waldman, 2010. "Competition, Monopoly, and Aftermarkets," The Journal of Law, Economics, and Organization, Oxford University Press, vol. 26(1), pages 54-91, April.
    20. Yue Liu & Rong Luo, 2023. "Network Effects and Multinetwork Sellers’ Dynamic Pricing in the U.S. Smartphone Market," Management Science, INFORMS, vol. 69(6), pages 3297-3318, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-01463925. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.