IDEAS home Printed from https://ideas.repec.org/a/wly/iecrev/v59y2018i4p1681-1731.html
   My bibliography  Save this article

The Dynamics Of Bertrand Price Competition With Cost‐Reducing Investments

Author

Listed:
  • Fedor Iskhakov
  • John Rust
  • Bertel Schjerning

Abstract

We extend the classic Bertrand duopoly model of price competition to a dynamic setting where competing duopolists invest in a stochastically improving production technology to “leapfrog” their rival and attain temporary low‐cost leadership. We find a huge multiplicity of Markov‐perfect equilibria (MPE) and show that when firms move simultaneously the set of all MPE payoffs is a triangle that includes monopoly payoffs and a symmetric zero mixed strategy payoff. When firms move asynchronously, the set of MPE payoffs is strictly within this triangle, but there still is a vast multiplicity of MPE, most of which involve leapfrogging.

Suggested Citation

  • Fedor Iskhakov & John Rust & Bertel Schjerning, 2018. "The Dynamics Of Bertrand Price Competition With Cost‐Reducing Investments," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(4), pages 1681-1731, November.
  • Handle: RePEc:wly:iecrev:v:59:y:2018:i:4:p:1681-1731
    DOI: 10.1111/iere.12317
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/iere.12317
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Doraszelski, Ulrich & Escobar, Juan, 2010. "A theory of regular Markov perfect equilibria in dynamic stochastic games: genericity, stability, and purification," Theoretical Economics, Econometric Society, vol. 5(3), September.
    2. Ulrich Doraszelski & Mark Satterthwaite, 2010. "Computable Markov‐perfect industry dynamics," RAND Journal of Economics, RAND Corporation, vol. 41(2), pages 215-243, June.
    3. Dan Kovenock & Raymond J. Deneckere, 1996. "Bertrand-Edgeworth duopoly with unit cost asymmetry (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 1-25.
    4. Audra J. Bowlus & Shannon Seitz, 2006. "Domestic Violence, Employment, And Divorce," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(4), pages 1113-1149, November.
    5. Ronald L. Goettler & Brett R. Gordon, 2011. "Does AMD Spur Intel to Innovate More?," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1141-1200.
    6. Giovannetti, Emanuele, 2001. "Perpetual Leapfrogging in Bertrand Duopoly," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(3), pages 671-696, August.
    7. F. M. Scherer, 1967. "Research and Development Resource Allocation Under Rivalry," The Quarterly Journal of Economics, Oxford University Press, vol. 81(3), pages 359-394.
    8. Routledge, Robert R., 2010. "Bertrand competition with cost uncertainty," Economics Letters, Elsevier, vol. 107(3), pages 356-359, June.
    9. Jennifer F. Reinganum, 1981. "On the Diffusion of New Technology: A Game Theoretic Approach," Review of Economic Studies, Oxford University Press, vol. 48(3), pages 395-405.
    10. Peter L. Swan, 1970. "Market Structure and Technological Progress: The Influence of Monopoly on Product Innovation," The Quarterly Journal of Economics, Oxford University Press, vol. 84(4), pages 627-638.
    11. Riordan, Michael H & Salant, David J, 1994. "Preemptive Adoptions of an Emerging Technology," Journal of Industrial Economics, Wiley Blackwell, vol. 42(3), pages 247-261, September.
    12. ANDERSON, Simon P. & de PALMA, André & THISSE, Jacques-François, 1992. "Interpretations of the logit discrete choice models and the theory of product differentiation," LIDAM Reprints CORE 1017, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Fudenberg, Drew & Gilbert, Richard & Stiglitz, Joseph & Tirole, Jean, 1983. "Preemption, leapfrogging and competition in patent races," European Economic Review, Elsevier, vol. 22(1), pages 3-31, June.
    14. Rosenkranz, Stephanie, 1997. "Quality improvements and the incentive to leapfrog," International Journal of Industrial Organization, Elsevier, vol. 15(2), pages 243-261, April.
    15. Rust, John, 1986. "When Is It Optimal to Kill Off the Market for Used Durable Goods?," Econometrica, Econometric Society, vol. 54(1), pages 65-86, January.
    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. Ulrich Doraszelski & Kenneth L. Judd, 2019. "Dynamic stochastic games with random moves," Quantitative Marketing and Economics (QME), Springer, vol. 17(1), pages 59-79, March.
    2. Fedor Iskhakov & John Rust & Bertel Schjerning, 2016. "Recursive Lexicographical Search: Finding All Markov Perfect Equilibria of Finite State Directional Dynamic Games," Review of Economic Studies, Oxford University Press, vol. 83(2), pages 658-703.
    3. Doraszelski, Ulrich & Escobar, Juan F., 2019. "Protocol invariance and the timing of decisions in dynamic games," Theoretical Economics, Econometric Society, vol. 14(2), May.
    4. Jacob Seifert, 2015. "Welfare effects of compulsory licensing," Journal of Regulatory Economics, Springer, vol. 48(3), pages 317-350, December.
    5. Ronald Goettler & Brett Gordon, 2014. "Competition and product innovation in dynamic oligopoly," Quantitative Marketing and Economics (QME), Springer, vol. 12(1), pages 1-42, March.

    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. Ron N. Borkovsky, 2017. "The timing of version releases: A dynamic duopoly model," Quantitative Marketing and Economics (QME), Springer, vol. 15(3), pages 187-239, September.
    2. Doraszelski, Ulrich & Escobar, Juan F., 2019. "Protocol invariance and the timing of decisions in dynamic games," Theoretical Economics, Econometric Society, vol. 14(2), May.
    3. Drew Fudenberg, 2015. "Tirole's Industrial Regulation and Organization Legacy in Economics," Scandinavian Journal of Economics, Wiley Blackwell, vol. 117(3), pages 771-800, July.
    4. John Rust & Bertel Schjerning & Fedor Iskhakov, 2012. "A Dynamic Model of Leap-Frogging Investments and Bertrand Price Competition," 2012 Meeting Papers 370, Society for Economic Dynamics.
    5. Ulrich Doraszelski & Kenneth L. Judd, 2019. "Dynamic stochastic games with random moves," Quantitative Marketing and Economics (QME), Springer, vol. 17(1), pages 59-79, March.
    6. Ron Borkovsky & Ulrich Doraszelski & Yaroslav Kryukov, 2012. "A dynamic quality ladder model with entry and exit: Exploring the equilibrium correspondence using the homotopy method," Quantitative Marketing and Economics (QME), Springer, vol. 10(2), pages 197-229, June.
    7. Helen Weeds, 2002. "Strategic Delay in a Real Options Model of R&D Competition," Review of Economic Studies, Oxford University Press, vol. 69(3), pages 729-747.
    8. C. Lanier Benkard & Przemyslaw Jeziorski & Gabriel Y. Weintraub, 2013. "Oblivious Equilibrium for Concentrated Industries," NBER Working Papers 19307, National Bureau of Economic Research, Inc.
    9. Brett Hollenbeck, 2020. "Horizontal mergers and innovation in concentrated industries," Quantitative Marketing and Economics (QME), Springer, vol. 18(1), pages 1-37, March.
    10. Maican, Florin G., 2012. "From Boom to Bust and Back Again: A dynamic analysis of IT services," Working Papers in Economics 543, University of Gothenburg, Department of Economics.
    11. Gonzalez-Diaz, Julio & Borm, Peter & Norde, Henk, 2007. "A silent battle over a cake," European Journal of Operational Research, Elsevier, vol. 177(1), pages 591-603, February.
    12. Stiglitz, Joseph E., 2015. "Leaders and followers: Perspectives on the Nordic model and the economics of innovation," Journal of Public Economics, Elsevier, vol. 127(C), pages 3-16.
    13. Karbowski, Adam, 2018. "Patents and Enterprise Innovation in Network Industries," EconStor Open Access Articles, ZBW - Leibniz Information Centre for Economics, pages 53-62.
    14. Harabi, Najib, 1994. "Technischer Fortschritt in der Schweiz: Empirische Ergebnisse aus industrieökonomischer Sicht [Technischer Fortschritt in der Schweiz:Empirische Ergebnisse aus industrieökonomischer Sicht]," MPRA Paper 6725, University Library of Munich, Germany.
    15. Ellis, Christopher J. & Silva, Emilson C. D., 1998. "British Bus Deregulation: Competition and Demand Coordination," Journal of Urban Economics, Elsevier, vol. 43(3), pages 336-361, May.
    16. Richard A. Jensen, 1980. "A Duopoly Model of the Adoption of an Innovation of Uncertainty Profitability," Discussion Papers 434, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    17. Ronald Goettler & Brett Gordon, 2014. "Competition and product innovation in dynamic oligopoly," Quantitative Marketing and Economics (QME), Springer, vol. 12(1), pages 1-42, March.
    18. Boyarchenko, Svetlana & Levendorskiĭ, Sergei, 2014. "Preemption games under Lévy uncertainty," Games and Economic Behavior, Elsevier, vol. 88(C), pages 354-380.
    19. Matsumura Toshihiro & Matsushima Noriaki, 2010. "When Small Firms Fight Back Against Large Firms in R&D Activities," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 10(1), pages 1-42, September.
    20. Masakazu Ishihara & Andrew T. Ching, 2019. "Dynamic Demand for New and Used Durable Goods Without Physical Depreciation: The Case of Japanese Video Games," Marketing Science, INFORMS, vol. 38(3), pages 392-416, May.

    More about this item

    JEL classification:

    • D92 - Microeconomics - - Micro-Based Behavioral Economics - - - Intertemporal Firm Choice, Investment, Capacity, and Financing
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

    Statistics

    Access and download statistics

    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:wly:iecrev:v:59:y:2018:i:4:p:1681-1731. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley Content Delivery). General contact details of provider: https://edirc.repec.org/data/deupaus.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.