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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

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    1. 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.
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    3. Fershtman, Chaim & Kamien, Morton I, 1987. "Dynamic Duopolistic Competition with Sticky Prices," Econometrica, Econometric Society, vol. 55(5), pages 1151-1164, September.
    4. 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.
    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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    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. Colombo, Luca & Labrecciosa, Paola, 2021. "A stochastic differential game of duopolistic competition with sticky prices," Journal of Economic Dynamics and Control, Elsevier, vol. 122(C).
    3. Margaret E. Slade, 1995. "Product Rivalry with multiple Strategic weapons: an Analysis of price and advertising Competition," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 4(3), pages 445-476, September.
    4. R. Cellini & L. Lambertini, 2008. "Weak and Strong Time Consistency in a Differential Oligopoly Game with Capital Accumulation," Journal of Optimization Theory and Applications, Springer, vol. 138(1), pages 17-26, July.
    5. 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.
    6. Katarzyna Kańska & Agnieszka Wiszniewska-Matyszkiel, 2022. "Dynamic Stackelberg duopoly with sticky prices and a myopic follower," Operational Research, Springer, vol. 22(4), pages 4221-4252, September.
    7. Miravete, Eugenio J., 2003. "Time-consistent protection with learning by doing," European Economic Review, Elsevier, vol. 47(5), pages 761-790, October.
    8. 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.
    9. 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.
    10. Driskill, Robert, 2001. "Durable goods oligopoly," International Journal of Industrial Organization, Elsevier, vol. 19(3-4), pages 391-413, March.
    11. Vassili Kolokoltsov & Wei Yang, 2012. "Turnpike Theorems for Markov Games," Dynamic Games and Applications, Springer, vol. 2(3), pages 294-312, September.
    12. 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.
    13. 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.
    14. Fell, Harrison, 2008. "Ex-vessel Pricing and IFQs: A Strategic Approach," RFF Working Paper Series dp-08-01, Resources for the Future.
    15. 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.
    16. 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.
    17. Robert Driskill & John Vrooman, 2016. "It’s Not Over ‘til the Fat Lady Sings," Journal of Sports Economics, , vol. 17(4), pages 354-376, May.
    18. R. Cellini & L. Lambertini, 2003. "Capacity Accumulation and Utilization in a Differential Duopoly Game," Working Papers 465, Dipartimento Scienze Economiche, Universita' di Bologna.
    19. Ganesh Manjhi & Meeta Keswani Mehra, 2019. "A Dynamic Analysis of Special Interest Politics and Electoral Competition," Dynamic Games and Applications, Springer, vol. 9(1), pages 142-164, March.
    20. 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.
    21. Luca Grilli & Michele Bisceglia, 2017. "A Duopoly with Common Renewable Resource and Incentives," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-20, December.
    22. Luca Grilli & Michele Bisceglia, 2017. "A differential game in a duopoly with instantaneous incentives," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 317-333, November.
    23. Gadi Fibich & Arieh Gavious & Oded Lowengart, 2003. "Explicit Solutions of Optimization Models and Differential Games with Nonsmooth (Asymmetric) Reference-Price Effects," Operations Research, INFORMS, vol. 51(5), pages 721-734, October.
    24. L. Lambertini, 2007. "Volatility forecasting for crude oil futures," Working Papers 598, Dipartimento Scienze Economiche, Universita' di Bologna.
    25. 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.

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