IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

Optgame 2.0: An Algorithm For Equilibrium Solutions Of N-Person Discrete-Time (Non-)Linear Dynamic Games

Listed author(s):
  • Reinhard Neck

    (University of Klagenfurt)

  • Doris A. Behrens

    (University of Klagenfurt)

We present the algorithm OPTGAME 2.0 to solve N-person discrete-time LQ games exactly, and discrete-time non-linear quadratic games approximately by means of an appropriate linearization procedure, where N>2. I.e., the objective function is assumed to be quadratic in the deviations of states and control variables from their respective desired target-values, and will be optimized for a pre-specified period of time subject to a nonlinear autonomous system. OPTGAME 2.0 allows the calculation of the Nash and Stackelberg equilibrium solutions, and the cooperative Pareto-optimal solutions for any number of players.Emanating from the informational basis of each player's decision, we distinguish between open-loop information patterns, where the player's strategies depend only on the initial state of the dynamic system, and feedback information patterns, where the strategies depend on the current state of the system (but not on the initial conditions). Deterministic dynamic game models can be solved by using essentially the same techniques as for solving deterministic optimal control models, but the choice of the solution technique determines the information pattern. I.e., the application of the minimum principle generates the open-loop solutions, while the application of the dynamic programming technique determines the feedback solutions.The algorithm OPTGAME 2.0 starts from computing a tentative path of the state vector from the nonlinear system equations - using the Gauss-Seidl algorithm - with a given tentative path for the control variables. Then the algorithm linearizes the system equations at the reference values obtained before, replacing the nonlinear autonomous system by a linear non-autonomous one. Then, the algorithm calculates numerically the Nash, Stackelberg, and Pareto solutions of non-linear, quadratic deterministic games (with a finite planing horizon) under open-loop and feedback information structure. This is done by use of the appropriate optimization technique corresponding to the desired information structure of the game, and yields so-called Riccati equations which can be solved by backward integration. Then, we derive by forward iteration the so-called feedback matrices, where further substitution of these matrices into linear relations in the preceding state variable delivers the values of the optimal control variables (expressed in feedback form) - as well as the optimal state values.The term äOPTGAME" denotes both, the computer algorithm and its implementation, where the implementation part consists of a set of procedures which are implemented in the programming language GAUSS. GAUSS is a high level matrix programming language specializing in commands, functions, and procedures for data analysis and statistical applications. This interplay is of special interest for the application of OPTGAME 2.0 in the field of optimal short-run and long-run fiscal policies towards the EMU. Furthermore, GAUSS includes a variety of routines which perform standard matrix operations, e.g. routines to calculate determinants, matrix inverses, decompositions, eigenvalues and eigenvectors, and condition numbers.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: no

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2000 with number 20.

in new window

Date of creation: 05 Jul 2000
Handle: RePEc:sce:scecf0:20
Contact details of provider: Postal:
CEF 2000, Departament d'Economia i Empresa, Universitat Pompeu Fabra, Ramon Trias Fargas, 25,27, 08005, Barcelona, Spain

Fax: +34 93 542 17 46
Web page:

More information through EDIRC

No references listed on IDEAS
You can help add them by filling out this form.

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:sce:scecf0:20. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.