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Weak and Strong Time Consistency in Differential Oligopoly Games with Capital Accumulation

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  • R. Cellini
  • L. Lambertini

Abstract

We illustrate two differential oligopoly games with capital accumulation where, alternatively, the accumulation dynamics of productive capacity is modelled either `a la Solow—Swan or `a la Ramsey. We show that in the first case the open-loop Nash equilibrium is only weakly time consistent, while in the second it is strongly so, although the Ramsey game is not state linear.

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  • R. Cellini & L. Lambertini, 2005. "Weak and Strong Time Consistency in Differential Oligopoly Games with Capital Accumulation," Working Papers 544, Dipartimento Scienze Economiche, Universita' di Bologna.
  • Handle: RePEc:bol:bodewp:544
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    References listed on IDEAS

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    1. Swan, Trevor W, 2002. "Economic Growth," The Economic Record, The Economic Society of Australia, vol. 78(243), pages 375-380, December.
    2. 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.
    3. repec:spr:joptap:v:126:y:2005:i:1:d:10.1007_s10957-005-2659-0 is not listed on IDEAS
    4. Fershtman, Chaim & Kamien, Morton I, 1987. "Dynamic Duopolistic Competition with Sticky Prices," Econometrica, Econometric Society, vol. 55(5), pages 1151-1164, September.
    5. R. Cellini & L. Lambertini, 2005. "R&D Incentives and Market Structure: Dynamic Analysis," Journal of Optimization Theory and Applications, Springer, vol. 126(1), pages 85-96, July.
    6. Calzolari, Giacomo & Lambertini, Luca, 2007. "Export restraints in a model of trade with capital accumulation," Journal of Economic Dynamics and Control, Elsevier, vol. 31(12), pages 3822-3842, December.
    7. R. Cellini & L. Lambertini, 2000. "Non-Linear Market Demand and Capital Accumulation in A Differential Oligopoly Game," Working Papers 372, Dipartimento Scienze Economiche, Universita' di Bologna.
    8. Gustav Feichtinger & Richard F. Hartl & Suresh P. Sethi, 1994. "Dynamic Optimal Control Models in Advertising: Recent Developments," Management Science, INFORMS, vol. 40(2), pages 195-226, February.
    9. Fershtman, Chaim & Muller, Eitan, 1984. "Capital accumulation games of infinite duration," Journal of Economic Theory, Elsevier, vol. 33(2), pages 322-339, August.
    10. R. Cellini & L. Lambertini, 2000. "Dynamic Oligopoly with Sticky Prices: Closed-Loop,Feedback and Open-Loop Solutions," Working Papers 393, Dipartimento Scienze Economiche, Universita' di Bologna.
    11. Dockner, Engelbert J. & Haug, Alfred A., 1990. "Tariffs and quotas under dynamic duopolistic competition," Journal of International Economics, Elsevier, vol. 29(1-2), pages 147-159, August.
    12. 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.
    13. 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.
    14. M. Baldini & L. Lambertini, 2002. "Profit Taxation and Capital Accumulation in Dynamic Oligopoly Models," Working Papers 435, Dipartimento Scienze Economiche, Universita' di Bologna.
    15. R. Cellini & L. Lambertini & G. Leitmann, 2005. "Degenerate Feedback and Time Consistency in Dynamic Games," Working Papers 535, Dipartimento Scienze Economiche, Universita' di Bologna.
    16. David M. Kreps & Jose A. Scheinkman, 1983. "Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 326-337, Autumn.
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    Cited by:

    1. Lambertini, Luca & Palestini, Arsen, 2014. "On the feedback solutions of differential oligopoly games with hyperbolic demand curve and capacity accumulation," European Journal of Operational Research, Elsevier, vol. 236(1), pages 272-281.
    2. Wirl, Franz, 2010. "Dynamic demand and noncompetitive intertemporal output adjustments," International Journal of Industrial Organization, Elsevier, vol. 28(3), pages 220-229, May.
    3. Lambertini, Luca & Mantovani, Andrea, 2006. "Identifying reaction functions in differential oligopoly games," Mathematical Social Sciences, Elsevier, vol. 52(3), pages 252-271, December.
    4. L. Lambertini, 2010. "On the Feedback Solution of a Differential Oligopoly Game with Hyperbolic Demand and Capacity Accumulation," Working Papers 692, Dipartimento Scienze Economiche, Universita' di Bologna.
    5. Dragone, Davide, 2009. "I am getting tired: Effort and fatigue in intertemporal decision-making," Journal of Economic Psychology, Elsevier, vol. 30(4), pages 552-562, August.
    6. Alessandra Buratto & Luca Grosset & Bruno Viscolani, 2012. "ε-Subgame Perfectness of an Open-Loop Stackelberg Equilibrium in Linear-State Games," Dynamic Games and Applications, Springer, vol. 2(3), pages 269-279, September.
    7. D. Dragone & L. Lambertini & A. Palestini, 2011. "On the feedback solution of a differential oligopoly game with capacity adjustment," Working Papers wp741, Dipartimento Scienze Economiche, Universita' di Bologna.

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