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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.
    2. 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.
    3. 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.
    4. 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.
    5. Kydland, Finn, 1977. "Equilibrium solutions in dynamic dominant-player models," Journal of Economic Theory, Elsevier, vol. 15(2), pages 307-324, August.
    6. 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.
    7. Kydland, Finn, 1975. "Noncooperative and Dominant Player Solutions in Discrete Dynamic Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 16(2), pages 321-335, June.
    8. 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.
    9. David Backus & John Driffill, 1985. "Rational Expectations and Policy Credibility Following a Change in Regime," Review of Economic Studies, Oxford University Press, vol. 52(2), pages 211-221.
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    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 Group Munich.
    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. 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.
    2. 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.
    3. Dennis, Richard, 2007. "Optimal Policy In Rational Expectations Models: New Solution Algorithms," Macroeconomic Dynamics, Cambridge University Press, vol. 11(1), pages 31-55, February.

    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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