Title
A numerical toolbox to solve **N**-player affine LQ open-loop differential games A numerical toolbox to solve **N**-player affine LQ open-loop differential games
Author
Faculty/Department
Faculty of Applied Economics
Publication type
article
Publication
Dordrecht ,
Subject
Economics
Computer. Automation
Source (journal)
Computational economics. - Dordrecht
Volume/pages
37(2011) :4 , p. 375-410
ISSN
0927-7099
ISI
000288253200003
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
We present an algorithm and a corresponding MATLAB numerical toolbox to solve any form of infinite-planning horizon affine linear quadratic open-loop differential games. By rewriting a specific application into the standard framework one can use the toolbox to calculate and verify the existence of both the open-loop non-cooperative Nash equilibrium (equilibria) and cooperative Pareto equilibrium (equilibria). In case there is more than one equilibrium for the non-cooperative case, the toolbox determines all solutions that can be implemented as a feedback strategy. Alternatively, the toolbox can apply a number of choice methods in order to discriminate between multiple equilibria. The user can predefine a set of coalition structures for which they would like to calculate the non-cooperative Nash solution(s). It is also possible to specify the relative importance of each player in any coalition structure. Furthermore, the toolbox offers plotting facilities as well as other options to analyse the outcome of the game. For instance, it is possible to disaggregate each players total loss into its contributing elements. The toolbox is available as a freeware from the authors of this paper.
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