Advanced Search
MyIDEAS: Login to save this paper or follow this series

The Dynamics of Bertrand Price Competition with Cost-Reducing Investments

Contents:

Author Info

  • Fedor Iskhakov

    (CEPAR, University of New South Wales)

  • John Rust

    (Georgetown University)

  • Bertel Schjerning

    (University of Copenhagen)

Abstract

We present a dynamic extension of the classic static model of Bertrand price competition that allows competing duopolists to undertake cost-reducing investments in an attempt to “leapfrog” their rival to attain low-cost leadership—at least temporarily. We show that leapfrogging occurs in equilibrium, resolving the Bertrand investment paradox., i.e. leapfrogging explains why firms have an ex ante incentive to undertake cost-reducing investments even though they realize that simultaneous investments to acquire the state of the art production technology would result in Bertrand price competition in the product market that drives their ex post profits to zero. Our analysis provides a new interpretation of “price wars”. Instead of constituting a punishment for a breakdown of tacit collusion, price wars are fully competitive outcomes that occur when one firm leapfrogs its rival to become the new low cost leader. We show that the equilibrium involves investment preemption only when the firms invest in a deterministically alternating fashion and technological progress is deterministic. We prove that when technological progress is deterministic and firms move in an alternating fashion, the game has a unique Markov perfect equilibrium. When technological progress is stochastic or if firms move simultaneously, equilibria are generally not unique. Unlike the static Bertrand model, the equilibria of the dynamic Bertrand model are generally inefficient. Instead of having too little investment in equilibrium, we show that duopoly investments generally exceed the socially optimum level. Yet, we show that when investment decisions are simultaneous there is a “monopoly” equilibrium when one firm makes all the investments, and this equilibrium is efficient. However, efficient non-monopoly equilibria also exist, demonstrating that it is possible for firms to achieve efficient dynamic coordination in their investments while their customers also benefit from technological progress in the form of lower prices.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.econ.ku.dk/english/research/publications/wp/dp_2013/1305.pdf
Download Restriction: no

Bibliographic Info

Paper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 13-05.

as in new window
Length: 57 pages
Date of creation: 15 Mar 2013
Date of revision:
Handle: RePEc:kud:kuiedp:1305

Contact details of provider:
Postal: Øster Farimagsgade 5, Building 26, DK-1353 Copenhagen K., Denmark
Phone: (+45) 35 32 30 10
Fax: +45 35 32 30 00
Email:
Web page: http://www.econ.ku.dk
More information through EDIRC

Related research

Keywords: duopoly; Bertrand-Nash price competition; Bertrand paradox; Bertrand investment paradox; leapfrogging; cost-reducing investments; technological improvement; dynamic models of competition; Markov-perfect equilibrium; tacit collusion; price wars; coordination and anti-coordination games; strategic preemption;

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

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.:
as in new window
  1. Juan Escobar & Ulrich Doraszelski, 2008. "A Theory of Regular Markov Perfect Equilibria\\in Dynamic Stochastic Games: Genericity, Stability, and Purification," 2008 Meeting Papers 453, Society for Economic Dynamics.
  2. Ulrich Doraszelski & Mark Satterthwaite, 2010. "Computable Markov-perfect industry dynamics," RAND Journal of Economics, RAND Corporation, vol. 41(2), pages 215-243.
  3. 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.
  4. Swan, Peter L, 1970. "Market Structure and Technological Progress: The Influence of Monopoly on Product Innovation," The Quarterly Journal of Economics, MIT Press, vol. 84(4), pages 627-38, November.
  5. Giovannetti, E., 2000. "Perpetual Leapfrogging in Bertrand Duopoly," Cambridge Working Papers in Economics 0012, Faculty of Economics, University of Cambridge.
  6. 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.
  7. Routledge, Robert R., 2010. "Bertrand competition with cost uncertainty," Economics Letters, Elsevier, vol. 107(3), pages 356-359, June.
  8. Rosenkranz, Stephanie, 1997. "Quality improvements and the incentive to leapfrog," International Journal of Industrial Organization, Elsevier, vol. 15(2), pages 243-261, April.
  9. 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.
  10. 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.
  11. Michael Riordan & David Salant, 1992. "Preemptive Adoptions of an Emerging Technology," Papers 0030, Boston University - Industry Studies Programme.
  12. Dan Kovenock & Raymond J. Deneckere, 1996. "Bertrand-Edgeworth duopoly with unit cost asymmetry (*)," Economic Theory, Springer, vol. 8(1), pages 1-25.
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 in new window

Cited by:
  1. Ronald Goettler & Brett Gordon, 2014. "Competition and product innovation in dynamic oligopoly," Quantitative Marketing and Economics, Springer, vol. 12(1), pages 1-42, March.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:kud:kuiedp:1305. 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: (Thomas Hoffmann).

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 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.