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An Anticipative Feedback Solution for Infinite-Horizon Linear-Quadratic Dynamic Stackelberg Games

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  • Baoline Chen and Peter Zadrozny

Abstract

The purpose of the paper is to derive and illustrate a new suboptimal-consistent feedback solution for infinite-horizon linear-quadratic dynamic Stackelberg games which is in the same solution space as the infinite-horizon dynamic programming feedback solution, but which puts the leader in a preferred equilibrium position. The idea for the solution comes from Kydland's (1977) suggestion to derive a consistent feedback solution (where "feedback" is understood in the general sense of setting a current control vector as a function of a predetermined state vector) for an infinite-horizon linear-quadratic dynamic Stackelberg game by varying coefficients in players' linear constant-coefficient decision rules. The proposed solution is derived for discrete- and continuous-time versions of the game and is called the anticipative feedback (AF) solution. The AF solution is illustrated with a numerical example of a duopoly model.

Suggested Citation

  • Baoline Chen and Peter Zadrozny, 2001. "An Anticipative Feedback Solution for Infinite-Horizon Linear-Quadratic Dynamic Stackelberg Games," Computing in Economics and Finance 2001 110, Society for Computational Economics.
    • Handle: RePEc:sce:scecf1:110
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    References listed on IDEAS

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    1. Barro, Robert J. & Gordon, David B., 1983. "Rules, discretion and reputation in a model of monetary policy," Journal of Monetary Economics, Elsevier, vol. 12(1), pages 101-121.
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    3. Miller, Marcus & Salmon, Mark, 1985. "Dynamic Games and the Time Inconsistency of Optimal Policy in Open Economies," Economic Journal, Royal Economic Society, vol. 95(380a), pages 124-137, Supplemen.
    4. Turnovsky, Stephen J & Basar, Tamer & d'Orey, Vasco, 1988. "Dynamic Strategic Monetary Policies and Coordination in Interdependent Economies," American Economic Review, American Economic Association, vol. 78(3), pages 341-361, June.
    5. Zadrozny, Peter, 1988. "A consistent, closed-loop solution for infinite-horizon, linear-quadratic, dynamic Stackelberg games," Journal of Economic Dynamics and Control, Elsevier, vol. 12(1), pages 155-159, March.
    6. David Backus & John Driffill, 1985. "Rational Expectations and Policy Credibility Following a Change in Regime," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(2), pages 211-221.
    7. Canzoneri, Matthew B & Gray, Jo Anna, 1985. "Monetary Policy Games and the Consequences of Non-cooperative Behavior," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(3), pages 547-564, October.
    8. Townsend, Robert M, 1983. "Forecasting the Forecasts of Others," Journal of Political Economy, University of Chicago Press, vol. 91(4), pages 546-588, August.
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    10. Fischer, Stanley, 1980. "Dynamic inconsistency, cooperation and the benevolent dissembling government," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 93-107, May.
    11. Baoline Chen & Peter A. Zadrozny, 2005. "Estimated U.S. Manufacturing Production Capital and Technology Based on an Estimated Dynamic Economic Model," CESifo Working Paper Series 1526, CESifo.
    12. Kydland, Finn E & Prescott, Edward C, 1977. "Rules Rather Than Discretion: The Inconsistency of Optimal Plans," Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 473-491, June.
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    Cited by:

    1. Dennis, Richard, 2007. "Optimal Policy In Rational Expectations Models: New Solution Algorithms," Macroeconomic Dynamics, Cambridge University Press, vol. 11(1), pages 31-55, February.
    2. Nie, Pu-yan & Chen, Li-hua & Fukushima, Masao, 2006. "Dynamic programming approach to discrete time dynamic feedback Stackelberg games with independent and dependent followers," European Journal of Operational Research, Elsevier, vol. 169(1), pages 310-328, February.
    3. David Yeung & Ovanes Petrosian, 2017. "Infinite Horizon Dynamic Games: A New Approach via Information Updating," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-23, December.

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    More about this item

    Keywords

    noncooperative dynamic games; solving Riccati-type nonlinear algebraic equations;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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