OPTGAME 2.0: An Algorithm for Equilibrium Solutions of N-Person Discrete-Time (Non-)Linear Dynamic Games
by
Doris Behrens
University of Klagenfurt, Inst of Economics and Business Adm
Coauthors: Reinhard Neck (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 along a reference path, 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). The term "OPTGAME" 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 – a high level matrix programming language specializing in commands, functions, and procedures for data analysis and statistical applications.

Date received: May 17, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafc-52.