An extension of the coordinate transformation method for open-loop nash equilibria

In Leitmann (Ref. 1), a coordinate transformation method was introduced to obtain global solutions for free problems in the calculus of variations. This direct method was extended and broadened in Carlson (Ref. 2) and later in Leitmann (Ref. 3). The applicability of the original work of Leitmann (Re...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2004-10, Vol.123 (1), p.27-47
Main Authors: CARLSON, D. A, LEITMANN, G
Format: Article
Language:English
Subjects:
Applied sciences
Calculus
Calculus of variations
Control theory
Coordinate transformations
Equilibrium
Exact sciences and technology
Game theory
Games
Mathematical programming
Operational research and scientific management
Operational research. Management science
Studies
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Summary:In Leitmann (Ref. 1), a coordinate transformation method was introduced to obtain global solutions for free problems in the calculus of variations. This direct method was extended and broadened in Carlson (Ref. 2) and later in Leitmann (Ref. 3). The applicability of the original work of Leitmann (Ref. 1) was further developed in Dockner and Leitmann (Ref. 4) to include the class of open-loop dynamic games. In the present work, we improve the results of Ref. 4 in two directions. First, we enlarge the class of open-loop dynamic games to permit coupling among the dynamic equations via the states of the players; second, we incorporate the modifications given in Refs. 2 and 3. Our results greatly increase the applicability of this method. An example arising from the harvesting of a renewable resource is presented to illustrate the utility of our results.
ISSN:0022-3239
1573-2878
DOI:10.1023/B:JOTA.0000043990.32923.ac