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Dynamic Model of R&D, Spillovers, and Efficiency of Bertrand and Cournot Equilibria

Author

Listed:
  • M. Breton

    (GERAD, CREF, and HEC Montréal)

  • A. Turki

    (HEC Montréal)

  • G. Zaccour

    (GERAD, CREF, and HEC Montréal)

Abstract

Using an infinite-horizon two-player differential game, we derive and compare Bertrand and Cournot equilibria for a differentiated duopoly engaging in the process of R&D competition. The main findings of this study are as follows. First, Bertrand competition is more efficient if either R&D productivity is low or products are very different. Second, Cournot competition is more efficient provided that R&D productivity is high, products are close substitutes, and spillovers are not close to zero. This last result is different from what has been obtained in the literature. Hence, this shows that considering a dynamic model and more general investment costs does have an impact on the efficiency results.

Suggested Citation

  • M. Breton & A. Turki & G. Zaccour, 2004. "Dynamic Model of R&D, Spillovers, and Efficiency of Bertrand and Cournot Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 123(1), pages 1-25, October.
    • Handle: RePEc:spr:joptap:v:123:y:2004:i:1:d:10.1023_b:jota.0000043989.95285.51
    DOI: 10.1023/B:JOTA.0000043989.95285.51
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    References listed on IDEAS

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    Cited by:

    1. F. Ben Abdelaziz & M. Ben Brahim & G. Zaccour, 2008. "R&D Equilibrium Strategies with Surfers," Journal of Optimization Theory and Applications, Springer, vol. 136(1), pages 1-13, January.
    2. Flavio M. Menezes & Jorge Pereira, 2017. "Emissions abatement R&D: Dynamic competition in supply schedules," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 19(4), pages 841-859, August.
    3. Lee, DongJoon & Choi, Kangsik & Nariu, Tatsuhiko, 2016. "Endogenous Choice of Price or Quantity Contract with Upstream R&D Investment: Linear Pricing and Two-part Tariff Contract with Bargaining," MPRA Paper 72752, University Library of Munich, Germany.
    4. Dawid, Herbert & Kopel, Michael & Kort, Peter M., 2013. "New product introduction and capacity investment by incumbents: Effects of size on strategy," European Journal of Operational Research, Elsevier, vol. 230(1), pages 133-142.
    5. Ahmad Reza Saboori Memar & Georg Götz, 2013. "R&D Incentives in Vertically Related Markets," MAGKS Papers on Economics 201307, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
    6. Samano, Mario & Santugini, Marc & Zaccour, Georges, 2017. "Dynamics in research joint ventures and R&D collaborations," Journal of Economic Dynamics and Control, Elsevier, vol. 77(C), pages 70-92.
    7. Jeroen Hinloopen & Jan Vandekerckhove, 2009. "Dynamic efficiency of Cournot and Bertrand competition: input versus output spillovers," Journal of Economics, Springer, vol. 98(2), pages 119-136, November.
    8. Ahmad Reza Saboori Memar, 2013. "Profitable Entry into an Unprofitable Market," MAGKS Papers on Economics 201306, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
    9. Jiafeng Gu, 2021. "Determinants of biopharmaceutical R&D expenditures in China: the impact of spatiotemporal context," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(8), pages 6659-6680, August.
    10. H. Dawid & M. Kopel & P. Kort, 2010. "Dynamic strategic interaction between an innovating and a non-innovating incumbent," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(4), pages 453-463, December.

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