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Slow and Steady Wins the Race: Approximating Nash Equilibria in Nonlinear Quadratic Tracking Games Steter Tropfen höhlt den Stein: Approximation von Nash Gleichgewichten in Nicht-linearen Dynamischen Spielen

Author

Listed:
  • Savin Ivan

    () (Chair for Economic Policy, Karlsruhe Institute of Technology, Karlsruhe, Germany)

  • Blueschke Dmitri

    () (Alpen-Adria-Universität Klagenfurt, Klagenfurt am Wörthersee, Klagenfurt, Austria)

  • Blueschke-Nikolaeva Viktoria

    () (Alpen-Adria-Universität Klagenfurt, Klagenfurt am Wörthersee, Klagenfurt, Austria)

Abstract

We propose a new method for solving nonlinear dynamic tracking games using a meta-heuristic approach. In contrast to ‘traditional’ methods based on linear-quadratic (LQ) techniques, this derivative-free method is very flexible with regard to the objective function specification. The proposed method is applied to a three-player dynamic game and tested versus a derivative-dependent method in approximating solutions of different game specifications. In particular, we consider a dynamic game between fiscal (played by national governments) and monetary policy (played by a central bank) in a monetary union. Apart from replicating results of the LQ-based techniques in a standard setting, we solve two ‘non-standard’ extensions of this game (dealing with an inequality constraint in a control variable and introducing asymmetry in penalties of the objective function), identifying both a cooperative Pareto and a non-cooperative open-loop Nash equilibria, where the traditional methods are not applicable. We, thus, demonstrate that the proposed method allows one to study more realistic problems and gain better insights for economic policy.

Suggested Citation

  • Savin Ivan & Blueschke Dmitri & Blueschke-Nikolaeva Viktoria, 2018. "Slow and Steady Wins the Race: Approximating Nash Equilibria in Nonlinear Quadratic Tracking Games Steter Tropfen höhlt den Stein: Approximation von Nash Gleichgewichten in Nicht-linearen Dynamischen ," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 238(6), pages 541-569, October.
  • Handle: RePEc:jns:jbstat:v:238:y:2018:i:6:p:541-569:n:2
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    Keywords

    dynamic games; Nash equilibrium; Pareto equilibrium; policy cooperation; 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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