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OPTGAME3: A Dynamic Game Solver and an Economic Example

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Advances in Dynamic Games

Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 13))

Abstract

In this paper we present the OPTGAME3 algorithm, which can be used to calculate equilibrium and optimum control solutions of dynamic games. The algorithm was programmed in C# and MATLAB and allows the calculation of approximate cooperative Pareto-optimal solutions and non-cooperative Nash and Stackelberg equilibrium solutions. In addition we present an application of the OPTGAME3 algorithm where we use a small stylized nonlinear two-country macroeconomic model of a monetary union for analysing the interactions between fiscal (governments) and monetary (common central bank) policy makers, assuming different objective functions of these decision makers. Several dynamic game experiments are run for different information patterns and solution concepts. We show how the policy makers react optimally to demand and supply shocks. Some comments are given about possible applications to the recent sovereign debt crisis in Europe.

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Notes

  1. 1.

    The source code of the OPTGAME3 algorithm is available from the authors on request.

  2. 2.

    For example, the central bank in a monetary union, which controls monetary policy, can also penalize “bad” fiscal policies of member countries.

  3. 3.

    Note that if convergence has not been obtained before k has reached its terminal value, then the iteration process terminates without succeeding in finding an equilibrium feedback solution.

  4. 4.

    The mathematical details are based on Behrens and Neck (2007) and reflect the calculations and proofs in Başar and Olsder (1999).

  5. 5.

    It is important to mention that we have a system with two simultaneous equations and two unknown parameters in step 2 ((2.20) and (2.21)). Therefore a system solver must be applied. In OPTGAME3, the Gauss–Seidel method is applied for this purpose.

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Acknowledgements

An earlier version of this paper was presented at the 15th ISDG Symposium on Dynamic Games and Applications. Thanks are due to very helpful comments and suggestions by participants at this symposium and by an anonymous referee.

Author information

Authors and Affiliations

  1. Department of Economics, Alpen-Adria-Universität Klagenfurt, Universitätsstrasse 65–67, 9020, Klagenfurt, Austria

    Dmitri Blueschke & Reinhard Neck

  2. Department of Controlling and Strategic Management, Alpen-Adria-Universität Klagenfurt, Universitätsstrasse 65–67, 9020, Klagenfurt, Austria

    Doris A. Behrens

Authors
  1. Dmitri Blueschke
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  2. Reinhard Neck
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  3. Doris A. Behrens
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Corresponding author

Correspondence to Reinhard Neck .

Editor information

Editors and Affiliations

  1. Institute of Entomology Dept. of Theoretical Ecology, Biology Centre AS CR, České Budějovice, Czech Republic

    Vlastimil Křivan

  2. GERAD, HEC Montréal, Montreal, Québec, Canada

    Georges Zaccour

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Blueschke, D., Neck, R., Behrens, D.A. (2013). OPTGAME3: A Dynamic Game Solver and an Economic Example. In: Křivan, V., Zaccour, G. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 13. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-02690-9_2

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