The Dynamics of Bertrand Price Competition with Cost-Reducing Investments
AbstractWe 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 InfoIf 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.
Bibliographic InfoPaper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 13-05.
Length: 57 pages
Date of creation: 15 Mar 2013
Date of revision:
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
Web page: http://www.econ.ku.dk
More information through EDIRC
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:
- D92 - Microeconomics - - Intertemporal Choice - - - 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-06-24 (All new papers)
- NEP-COM-2013-06-24 (Industrial Competition)
- NEP-IND-2013-06-24 (Industrial Organization)
- NEP-MIC-2013-06-24 (Microeconomics)
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.:
- Riordan, Michael H & Salant, David J, 1994.
"Preemptive Adoptions of an Emerging Technology,"
Journal of Industrial Economics,
Wiley Blackwell, vol. 42(3), pages 247-61, September.
- Giovannetti, E., 2000.
"Perpetual Leapfrogging in Bertrand Duopoly,"
Cambridge Working Papers in Economics
0012, Faculty of Economics, University of Cambridge.
- Routledge, Robert R., 2010. "Bertrand competition with cost uncertainty," Economics Letters, Elsevier, vol. 107(3), pages 356-359, June.
- 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.
- 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.
- Audra J. Bowlus & Shannon N. Seitz, 2002. "Domestic Violence, Employment and Divorce," Working Papers 1007, Queen's University, Department of Economics.
- Audra Bowlus & Shannon Seitz, 2005. "Domestic Violence, Employment, and Divorce," Working Papers 1075, Queen's University, Department of Economics.
- Rosenkranz, Stephanie, 1997. "Quality improvements and the incentive to leapfrog," International Journal of Industrial Organization, Elsevier, vol. 15(2), pages 243-261, April.
- 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.
- 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.
- Doraszelski, Ulrich & Escobar, Juan, 2008. "A Theory of Regular Markov Perfect Equilibria in Dynamic Stochastic Games: Genericity, Stability, and Purification," CEPR Discussion Papers 6805, C.E.P.R. Discussion Papers.
- 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.
- Brett Gordon & Ronald Goettler, 2010.
"Does AMD spur Intel to innovate more?,"
2010 Meeting Papers
151, Society for Economic Dynamics.
- Dan Kovenock & Raymond J. Deneckere, 1996. "Bertrand-Edgeworth duopoly with unit cost asymmetry (*)," Economic Theory, Springer, vol. 8(1), pages 1-25.
- 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.
- Ulrich Doraszelski & Mark Satterthwaite, 2010. "Computable Markov-perfect industry dynamics," RAND Journal of Economics, RAND Corporation, vol. 41(2), pages 215-243.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Thomas Hoffmann).
If references are entirely missing, you can add them using this form.