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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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    1. Dastidar, Krishnendu Ghosh, 1997. "Comparing Cournot and Bertrand in a Homogeneous Product Market," Journal of Economic Theory, Elsevier, vol. 75(1), pages 205-212, July.
    2. Delbono, Flavio & Denicolo, Vincenzo, 1990. "R & D investment in a symmetric and homogeneous oligopol : Bertrand vs Cournot," International Journal of Industrial Organization, Elsevier, vol. 8(2), pages 297-313, June.
    3. Reynolds, Stanley S., 1991. "Dynamic oligopoly with capacity adjustment costs," Journal of Economic Dynamics and Control, Elsevier, vol. 15(3), pages 491-514, July.
    4. Okuguchi, Koji, 1987. "Equilibrium prices in the Bertrand and Cournot oligopolies," Journal of Economic Theory, Elsevier, vol. 42(1), pages 128-139, June.
    5. Amir, Rabah & Jin, Jim Y., 2001. "Cournot and Bertrand equilibria compared: substitutability, complementarity and concavity," International Journal of Industrial Organization, Elsevier, vol. 19(3-4), pages 303-317, March.
    6. Tanaka, Yasuhito, 2001. "Profitability of price and quantity strategies in an oligopoly," Journal of Mathematical Economics, Elsevier, vol. 35(3), pages 409-418, June.
    7. Qiu, Larry D., 1997. "On the Dynamic Efficiency of Bertrand and Cournot Equilibria," Journal of Economic Theory, Elsevier, vol. 75(1), pages 213-229, July.
    8. Leonard Cheng, 1985. "Comparing Bertrand and Cournot Equilibria: A Geometric Approach," RAND Journal of Economics, The RAND Corporation, vol. 16(1), pages 146-152, Spring.
    9. Symeonidis, George, 2003. "Comparing Cournot and Bertrand equilibria in a differentiated duopoly with product R&D," International Journal of Industrial Organization, Elsevier, vol. 21(1), pages 39-55, January.
    10. Nirvikar Singh & Xavier Vives, 1984. "Price and Quantity Competition in a Differentiated Duopoly," RAND Journal of Economics, The RAND Corporation, vol. 15(4), pages 546-554, Winter.
    11. Hackner, Jonas, 2000. "A Note on Price and Quantity Competition in Differentiated Oligopolies," Journal of Economic Theory, Elsevier, vol. 93(2), pages 233-239, August.
    12. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, October.
    13. Reynolds, Stanley S, 1987. "Capacity Investment, Preemption and Commitment in an Infinite Horizon Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(1), pages 69-88, February.
    14. Vives, Xavier, 1985. "On the efficiency of Bertrand and Cournot equilibria with product differentation," Journal of Economic Theory, Elsevier, vol. 36(1), pages 166-175, June.
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