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An anticipative feedback solution for the infinite-horizon, linear-quadratic, dynamic, Stackelberg game

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  • Chen, Baoline
  • Zadrozny, Peter A.

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.
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Suggested Citation

  • Chen, Baoline & Zadrozny, Peter A., 2002. "An anticipative feedback solution for the infinite-horizon, linear-quadratic, dynamic, Stackelberg game," Journal of Economic Dynamics and Control, Elsevier, vol. 26(9-10), pages 1397-1416, August.
    • Handle: RePEc:eee:dyncon:v:26:y:2002:i:9-10:p:1397-1416
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    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.
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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.

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    More about this item

    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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