An Extension of the Coordinate Transformation Method for Open-Loop Nash Equilibria

D. A. Carlson and G. Leitmann
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D. A. Carlson: University of Toledo
G. Leitmann: University of California

Journal of Optimization Theory and Applications, 2004, vol. 123, issue 1, No 2, 27-47

Abstract: Abstract 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.

Keywords: Calculus of variations; coordinate transformations; open-loop Nash equilibrium; Nash equilibria; dynamics games (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (3)

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DOI: 10.1023/B:JOTA.0000043990.32923.ac

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