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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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    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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