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Slow and steady wins the race: approximating Nash equilibria in nonlinear quadratic tracking games

Author

Listed:
  • Dimitri Blueschke

    (Alpen-Adria Universität Klagenfurt, Austria)

  • Viktoria Blüschke-Nikolaeva

    (Alpen-Adria Universität Klagenfurt, Austria)

  • Ivan Savin

    (Chair of Microeconomics, Friedrich Schiller University Jena, Germany, and Chair for Economic Policy, Karlsruhe Institute of Technology, Germany, and Bureau d'Economie Theorique et Appliquee, France)

Abstract

We propose a meta-heuristic approach for solving nonlinear dynamic tracking games. In contrast to more 'traditional' methods based on linear-quadratic (LQ) techniques, this derivative-free method is very flexible (e.g. to introduce inequality constraints). The meta-heuristic is applied to a three-player dynamic game and tested versus derivative-dependent method in approximating Nash solution in different game specifications. We demonstrate the superiority of the proposed approach in identifying Nash equilibria, where LQ methods are not applicable.

Suggested Citation

  • Dimitri Blueschke & Viktoria Blüschke-Nikolaeva & Ivan Savin, 2015. "Slow and steady wins the race: approximating Nash equilibria in nonlinear quadratic tracking games," Jena Economics Research Papers 2015-011, Friedrich-Schiller-University Jena.
    • Handle: RePEc:jrp:jrpwrp:2015-011
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    File URL: https://oweb.b67.uni-jena.de/Papers/jerp2015/wp_2015_011.pdf
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    References listed on IDEAS

    as
    1. Reinhard Neck & Dmitri Blueschke, 2014. "“Haircuts” for the EMU periphery: virtue or vice?," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 41(2), pages 153-175, May.
    2. Blueschke, D. & Blueschke-Nikolaeva, V. & Savin, I., 2013. "New insights into optimal control of nonlinear dynamic econometric models: Application of a heuristic approach," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 821-837.
    3. Dmitri Blueschke & Ivan Savin, 2015. "No such thing like perfect hammer: comparing different objective function specifications for optimal control," Jena Economics Research Papers 2015-005, Friedrich-Schiller-University Jena.
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    Cited by:

    1. D. Blueschke & I. Savin, 2017. "No such thing as a perfect hammer: comparing different objective function specifications for optimal control," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(2), pages 377-392, June.
    2. D. Blueschke & I. Savin & V. Blueschke-Nikolaeva, 2020. "An Evolutionary Approach to Passive Learning in Optimal Control Problems," Computational Economics, Springer;Society for Computational Economics, vol. 56(3), pages 659-673, October.

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    More about this item

    Keywords

    Dynamic games; Nash equilibrium; Differential Evolution;
    All these keywords.

    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
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • E61 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Policy Objectives; Policy Designs and Consistency; Policy Coordination

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