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

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  • Chaim Fershtman
  • Morton I. Kamien

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.
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Suggested Citation

  • Chaim Fershtman & Morton I. Kamien, 1987. "Turnpike Properties in a Finite Horizon Differential Game: Dynamic Duopoly with Sticky Prices," Discussion Papers 746, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:746
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    References listed on IDEAS

    as
    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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