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Turnpike Properties in a Finite-Horizon Differential Game: Dynamic Duopoly with Sticky Prices

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  • Fershtman, Chaim
  • Kamien, Morton I

Abstract

The authors study the equilibrium price paths of a finite-horizon dynamic duopoly model in which the market price does not have to adjust instantaneously in response to changes in the quantity supplied. A complete analysis of the feedback Nash equilibrium of a finite-horizon linear quadratic differential game with a control constraint is presented. Two equilibrium price paths are identified and it is shown that they both remain close to the infinite-horizon, globally asymptotically stable, stationary equilibrium except for some initial and final time. Copyright 1990 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Suggested Citation

  • 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.
  • Handle: RePEc:ier:iecrev:v:31:y:1990:i:1:p:49-60
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    References listed on IDEAS

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    1. Fershtman, Chaim & Kamien, Morton I, 1987. "Dynamic Duopolistic Competition with Sticky Prices," Econometrica, Econometric Society, vol. 55(5), pages 1151-1164, September.
    2. Driskill, Robert A. & McCafferty, Stephen, 1989. "Dynamic duopoly with adjustment costs: A differential game approach," Journal of Economic Theory, Elsevier, vol. 49(2), pages 324-338, December.
    3. Brock, William A. & Scheinkman, JoseA., 1976. "Global asymptotic stability of optimal control systems with applications to the theory of economic growth," Journal of Economic Theory, Elsevier, vol. 12(1), pages 164-190, February.
    4. David Cass, 1964. "Optimum Economic Growth in an Aggregative Model of Capital Accumulation: A Turnpike Theorem," Cowles Foundation Discussion Papers 178, Cowles Foundation for Research in Economics, Yale University.
    5. Fershtman, Chaim & Muller, Eitan, 1986. "Turnpike properties of capital accumulation games," Journal of Economic Theory, Elsevier, vol. 38(1), pages 167-177, February.
    6. 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.
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    Citations

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    Cited by:

    1. Agnieszka Wiszniewska-Matyszkiel & Marek Bodnar & Fryderyk Mirota, 2015. "Dynamic Oligopoly with Sticky Prices: Off-Steady-state Analysis," Dynamic Games and Applications, Springer, vol. 5(4), pages 568-598, December.
    2. Miravete, Eugenio J., 2003. "Time-consistent protection with learning by doing," European Economic Review, Elsevier, vol. 47(5), pages 761-790, October.
    3. L. Lambertini, 2010. "Oligopoly with Hyperbolic Demand: A Differential Game Approach," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 108-119, April.
    4. Cellini, Roberto & Lambertini, Luca, 2007. "A differential oligopoly game with differentiated goods and sticky prices," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1131-1144, January.
    5. repec:spr:decfin:v:40:y:2017:i:1:d:10.1007_s10203-017-0189-5 is not listed on IDEAS
    6. Roberto Cellini & Luca Lambertini, 2006. "Workers’ enterprises are not perverse: differential oligopoly games with sticky price," Review of Economic Design, Springer;Society for Economic Design, vol. 10(3), pages 233-248, December.
    7. 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.
    8. L. Lambertini, 2007. "Volatility forecasting for crude oil futures," Working Papers 598, Dipartimento Scienze Economiche, Universita' di Bologna.
    9. Fan, Ming & Kumar, Subodha & Whinston, Andrew B., 2009. "Short-term and long-term competition between providers of shrink-wrap software and software as a service," European Journal of Operational Research, Elsevier, vol. 196(2), pages 661-671, July.
    10. 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.
    11. Vassili Kolokoltsov & Wei Yang, 2012. "Turnpike Theorems for Markov Games," Dynamic Games and Applications, Springer, vol. 2(3), pages 294-312, September.
    12. Henry Thille & Margaret E. Slade, 2000. "Forward trading and adjustment costs in Cournot markets," Cahiers d'Économie Politique, Programme National Persée, vol. 37(1), pages 177-195.
    13. Slade, Margaret E., 1999. "Sticky prices in a dynamic oligopoly: An investigation of (s,S) thresholds," International Journal of Industrial Organization, Elsevier, vol. 17(4), pages 477-511, May.
    14. repec:wsi:igtrxx:v:19:y:2017:i:04:n:s0219198917500189 is not listed on IDEAS
    15. repec:spr:joptap:v:138:y:2008:i:1:d:10.1007_s10957-008-9432-0 is not listed on IDEAS
    16. Fell, Harrison, 2008. "Ex-vessel Pricing and IFQs: A Strategic Approach," Discussion Papers dp-08-01, Resources For the Future.
    17. R. Cellini & L. Lambertini, 2002. "Advertising with Spillover Effects in a Differential Oligopoly Game With Differentiated Goods," Working Papers 430, Dipartimento Scienze Economiche, Universita' di Bologna.
    18. R. Cellini & L. Lambertini, 2002. "Price vs Quantity in a Dynamic Duopoly Game with Capacity Accumulation," Working Papers 449, Dipartimento Scienze Economiche, Universita' di Bologna.

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