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Capacity Accumulation and Utilization in a Differential Duopoly Game

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  • R. Cellini
  • L. Lambertini

Abstract

We present a different duopoly game with capacity accumulation, where firms control investment effords and sales, which can be at most equal to the respective installed capacities at any point of time. We use, alternatively, inverse and direct demand functions with product differentiation, recalling Cournot and Bertrand competition. We show that, at the subgame perfect steady state equilibria, Cournot and Bertrand profits do not coincide, unless the game is quasi-static, which happens if capacity does not depreciate over time.

Suggested Citation

  • R. Cellini & L. Lambertini, 2003. "Capacity Accumulation and Utilization in a Differential Duopoly Game," Working Papers 465, Dipartimento Scienze Economiche, Universita' di Bologna.
    • Handle: RePEc:bol:bodewp:465
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    1. Fershtman, Chaim & Kamien, Morton I, 1990. "Turnpike Properties in a Finite-Horizon Differential Game: Dynamic Duopoly with Sticky Prices," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(1), pages 49-60, February.
    2. Fershtman, Chaim & Kamien, Morton I, 1987. "Dynamic Duopolistic Competition with Sticky Prices," Econometrica, Econometric Society, vol. 55(5), pages 1151-1164, September.
    3. R. Cellini & L. Lambertini, 2001. "Differential Oligopoly Games where the Closed-Loop Memoryless and Open-Loop Equilibria Coincide," Working Papers 402, Dipartimento Scienze Economiche, Universita' di Bologna.
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    5. 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.
    6. Fudenberg, Drew & Tirole, Jean, 1983. "Capital as a commitment: Strategic investment to deter mobility," Journal of Economic Theory, Elsevier, vol. 31(2), pages 227-250, December.
    7. Levitan, Richard & Shubik, Martin, 1972. "Price Duopoly and Capacity Constraints," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(1), pages 111-122, February.
    8. Fershtman, Chaim & Muller, Eitan, 1984. "Capital accumulation games of infinite duration," Journal of Economic Theory, Elsevier, vol. 33(2), pages 322-339, August.
    9. Osborne, Martin J. & Pitchik, Carolyn, 1986. "Price competition in a capacity-constrained duopoly," Journal of Economic Theory, Elsevier, vol. 38(2), pages 238-260, April.
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    11. 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.
    12. Cellini, Roberto & Lambertini, Luca, 1998. "A Dynamic Model of Differentiated Oligopoly with Capital Accumulation," Journal of Economic Theory, Elsevier, vol. 83(1), pages 145-155, November.
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    2. Villeneuve, Bertrand & Zhang, Vanessa Yanhua, 2008. "A Case for Affirmative Action in Competition Policy," MPRA Paper 9700, University Library of Munich, Germany.
    3. Bertrand Villeneuve & Vanessa Yanhua Zhang, 2013. "Industry Restructuring: A Case for Affirmative Action," Annals of Economics and Statistics, GENES, issue 109-110, pages 179-201.

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