IDEAS home Printed from https://ideas.repec.org/p/sap/wpaper/wp37.html
   My bibliography  Save this paper

Perpetual leapfrogging in Bertrand duopoly

Author

Listed:
  • Emanuele Giovannetti

Abstract

In this paper we focus on the intertemporal aspects of technological adoption. We consider a simplified model: firms produce an homogeneous good and adoption decisions concern a cost reducing technology. We focus on the issue of industrial leadership reversal. Imagine an industry facing a sequence of cost reducing innovations; the appearance of newer generations of PC processors provides a good example of the sort of improvements we have in mind. Individual firms can upgrade by adopting the most recent improvement. This improvement comes at a cost, for example, of installing the new processors. Will firms choose to make these costly adoptions? How do adoption rates depend on the product market competition? Which adoption patterns will be sustainable in equilibrium? Will these adoption strategies reduce aggressive competition? We consider a duopoly where firms set prices, i.e. there is Bertrand competition in the product market. In an intertemporal, infinite horizon setting, firms can adopt alternative and complicated dynamic adoption strategies. We study Markov Perfect equilibria (MPE’s) and in addition restrict attention to equilibria with relatively simple but economically relevant patterns. These are: 1) Alternating adoptions and 2) Increasing asymmetry. An increasing asymmetry pattern of adoptions is such that the firm with the lowest unit cost adopts, while the high cost firm does not, so that existing cost asymmetry is reinforced. An alternating adoptions pattern is such that the firm with high unit cost adopts, while the low cost firm does not, existing cost asymmetry is reversed and leapfrogging takes place. We find that if adoption is profitable at a given date, and the price elasticity of demand is greater than, or equal to, one, then no asymmetry can be absorbing and technological adoption goes on forever through an infinite sequence of leapfroggings. For this case we characterize the adoption cost region where a pattern of alternating adoptions is an MPE. In this setting increasing asymmetry is never an MPE. Perpetual leapfrogging emerges therefore as a set of simple adoption strategies allowing implicit and sustainable coordination between two firms. Such coordination helps avoiding the most aggressive aspects of duopolistic price competition. Only with high price elasticity, and a market size large enough compared to adoption costs, this goes on forever. If adoption is profitable at a given date but the elasticity of demand is below one, there is a date in which the adoption process will stop. Alternating adoptions up to this date is an MPE for a range of adoption costs. Increasing asymmetry can also be an equilibrium in this case, but under very restrictive conditions. In an oligopolistic industry demand conditions play an essential role in determining both the continuation or the end of the technological adoption and the identity of the adopters. When adoption continues, long run technological improvements are only made by high cost firms, which emerge as the engine of productivity growth. This is mainly due to the nature of the incentives for the adoption of a new technology under Bertand competition. For any downward sloping demand function the increments in period profits, due to the adoption of a new cost reducing technology, are larger for the follower than for the leader, because market demand when the follower adopts is higher than when the leader adopts. In this last case there is, indeed, a higher equilibrium price2. With isoelastic demand functions the value of the elasticity determines whether the adoption process will go on forever or not. With more general demand functions one would need to study the limit behaviour of the profits’ increments, due to adoption, when the equilibrium price tends to zero. Only if demand grows proportionally faster than the decrease of the price-cost margin, adoption of new technologies can go on forever. After a brief review of some related literature, the remainder of the paper is organized as follows: in section 2 we describe the model industry: market demand, technology evolution and costs, and firms’ decision sets and objective functions. In section 3 we analyse adoption decisions in a Bertrand duopoly, first with myopic firms and then with discounting. Finally section 4 contains the conclusions of the paper. All the proofs are contained in the appendix.

Suggested Citation

  • Emanuele Giovannetti, 1999. "Perpetual leapfrogging in Bertrand duopoly," Working Papers 37, University of Rome La Sapienza, Department of Public Economics.
  • Handle: RePEc:sap:wpaper:wp37
    as

    Download full text from publisher

    File URL: https://web.uniroma1.it/dip_ecodir/sites/default/files/wpapers/wp37.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jennifer F. Reinganum, 1985. "Innovation and Industry Evolution," The Quarterly Journal of Economics, Oxford University Press, vol. 100(1), pages 81-99.
    2. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
    3. 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.
    4. Kapur, Sandeep, 1995. "Markov perfect equilibria in an N-player war of attrition," Economics Letters, Elsevier, vol. 47(2), pages 149-154, February.
    5. Christopher Harris & John Vickers, 1987. "Racing with Uncertainty," Review of Economic Studies, Oxford University Press, vol. 54(1), pages 1-21.
    6. Kapur, Sandeep, 1995. "Technological Diffusion with Social Learning," Journal of Industrial Economics, Wiley Blackwell, vol. 43(2), pages 173-195, June.
    7. Tom Lee & Louis L. Wilde, 1980. "Market Structure and Innovation: A Reformulation," The Quarterly Journal of Economics, Oxford University Press, vol. 94(2), pages 429-436.
    8. Christopher Harris & John Vickers, 1985. "Perfect Equilibrium in a Model of a Race," Review of Economic Studies, Oxford University Press, vol. 52(2), pages 193-209.
    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. Furukawa, Yuichi, 2012. "Perpetual leapfrogging in international competition," MPRA Paper 40126, University Library of Munich, Germany, revised Jul 2012.
    2. Alfredo Garcia & Barry Horowitz, 2007. "The potential for underinvestment in internet security: implications for regulatory policy," Journal of Regulatory Economics, Springer, vol. 31(1), pages 37-55, February.
    3. Yuichi Furukawa, 2015. "Leapfrogging cycles in international competition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(2), pages 401-433, June.
    4. Diodato, Dario & Malerba, Franco & Morrison, Andrea, 2018. "The made-in effect and leapfrogging: A model of leadership change for products with country-of-origin bias," European Economic Review, Elsevier, vol. 101(C), pages 297-329.
    5. Lee, Jeongsik & Kim, Byung-Cheol & Lim, Young-Mo, 2011. "Dynamic competition in technological investments: An empirical examination of the LCD panel industry," International Journal of Industrial Organization, Elsevier, vol. 29(6), pages 718-728.
    6. Ibsen, Alexander Z., 2009. "The politics of airplane production: The emergence of two technological frames in the competition between Boeing and Airbus," Technology in Society, Elsevier, vol. 31(4), pages 342-349.
    7. James G. Mulligan & Nilotpal Das, 2005. "Persistent Adoption of Time-Saving Process Innovations," Working Papers 05-03, University of Delaware, Department of Economics.
    8. Giovannetti, Emanuele & Piga, Claudio A., 2017. "The contrasting effects of active and passive cooperation on innovation and productivity: Evidence from British local innovation networks," International Journal of Production Economics, Elsevier, vol. 187(C), pages 102-112.
    9. 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.
    10. Doraszelski, Ulrich & Escobar, Juan F., 2019. "Protocol invariance and the timing of decisions in dynamic games," Theoretical Economics, Econometric Society, vol. 14(2), May.
    11. Furukawa, Yuichi & Takarada, Yasuhiro, 2013. "Technological change and international interaction in environmental policies," MPRA Paper 44047, University Library of Munich, Germany.

    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. Shakun D. Mago & Roman M. Sheremeta, 2017. "Multi‐battle Contests: An Experimental Study," Southern Economic Journal, John Wiley & Sons, vol. 84(2), pages 407-425, October.
    2. Daron Acemoglu & Ufuk Akcigit, 2006. "State-Dependent Intellectual Property Rights Policy," NBER Working Papers 12775, National Bureau of Economic Research, Inc.
    3. Konrad, Kai A. & Kovenock, Dan, 2009. "Multi-battle contests," Games and Economic Behavior, Elsevier, vol. 66(1), pages 256-274, May.
    4. Kimbrough, Erik O. & Laughren, Kevin & Sheremeta, Roman, 2020. "War and conflict in economics: Theories, applications, and recent trends," Journal of Economic Behavior & Organization, Elsevier, vol. 178(C), pages 998-1013.
    5. Denter, Philipp & Sisak, Dana, 2015. "Do polls create momentum in political competition?," Journal of Public Economics, Elsevier, vol. 130(C), pages 1-14.
    6. Steinmetz, Alexander, 2010. "Competition, innovation, and the effect of knowledge accumulation," W.E.P. - Würzburg Economic Papers 81, University of Würzburg, Chair for Monetary Policy and International Economics.
    7. Kaplan, Todd R. & Luski, Israel & Wettstein, David, 2003. "Innovative activity and sunk cost," International Journal of Industrial Organization, Elsevier, vol. 21(8), pages 1111-1133, October.
    8. Robert M. Hunt, 2004. "Patentability, Industry Structure, and Innovation," Journal of Industrial Economics, Wiley Blackwell, vol. 52(3), pages 401-425, September.
    9. Häfner, Samuel, 2017. "A tug-of-war team contest," Games and Economic Behavior, Elsevier, vol. 104(C), pages 372-391.
    10. Subhasish M. Chowdhury & Patricia Esteve-González & Anwesha Mukherjee, 2020. "Heterogeneity, Leveling the Playing Field, and Affirmative Action in Contests," Economics Series Working Papers 915, University of Oxford, Department of Economics.
    11. Mehrez, Abraham & Justman, Moshe, 2001. "On the efficiency of the parallel path R&D approach: a stochastic game analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 57(1), pages 19-28.
    12. Hélène Halmenschlager, 2004. "Les externalités de diffusion du savoir-faire permettent-elles de rattraper le retard dans les courses à l'innovation ?," Recherches économiques de Louvain, De Boeck Université, vol. 70(3), pages 341-361.
    13. Czarnitzki, Dirk & Kraft, Kornelius, 2004. "An empirical test of the asymmetric models on innovative activity: who invests more into R&D, the incumbent or the challenger?," Journal of Economic Behavior & Organization, Elsevier, vol. 54(2), pages 153-173, June.
    14. Hoppe, Heidrun C. & Lehmann-Grube, Ulrich, 2005. "Innovation timing games: a general framework with applications," Journal of Economic Theory, Elsevier, vol. 121(1), pages 30-50, March.
    15. 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.
    16. Richard Gilbert, 2006. "Looking for Mr. Schumpeter: Where Are We in the Competition-Innovation Debate?," NBER Chapters, in: Innovation Policy and the Economy, Volume 6, pages 159-215, National Bureau of Economic Research, Inc.
    17. Emin Karagözoglu & Cagri Saglam & Agah R. Turan, 2020. "Tullock Brings Perseverance and Suspense to Tug-of-War," CESifo Working Paper Series 8103, CESifo.
    18. Boone, Jan, 2001. "Intensity of competition and the incentive to innovate," International Journal of Industrial Organization, Elsevier, vol. 19(5), pages 705-726, April.
    19. Aldieri, Luigi & Aprile, Maria Carmela & Vinci, Concetto Paolo, 2015. "R&D Spillovers Effects on strategic behaviour of Large International Firms," MPRA Paper 63402, University Library of Munich, Germany.
    20. Uwe Cantner & Werner Güth & Andreas Nicklisch & Torsten Weiland, 2009. "Competition In Product Design: An Experiment Exploring Innovation Behavior," Metroeconomica, Wiley Blackwell, vol. 60(4), pages 724-752, November.

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • O33 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Technological Change: Choices and Consequences; Diffusion Processes
    • 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:sap:wpaper:wp37. 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: . General contact details of provider: https://edirc.repec.org/data/dprosit.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 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: Luisa Giuriato (email available below). General contact details of provider: https://edirc.repec.org/data/dprosit.html .

    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.