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A Direct Method for Open-Loop Dynamic Games for Affine Control Systems

In: Dynamic Games: Theory and Applications

Author

Listed:
  • Dean A. Carlson
  • George Leitmann

Abstract

Recently in Carlson and Leitmann (2004) some improvements on Leitmann's direct method, first presented for problems in the calculus of variations in Leitmann (1967), for open-loop dynamic games in Dockner and Leitmann (2001) were given. In these papers each player has its own state which it controls with its own control inputs. That is, there is a state equation for each player. However, many applications involve the players competing for a single resource (e.g., two countries competing for a single species of fish). In this note we investigate the Utility of the direct method for a class of games whose dynamics are described by a single equation for which the state dynamics are affine in the players strategies. An illustrative example is also presented

Suggested Citation

  • Dean A. Carlson & George Leitmann, 2005. "A Direct Method for Open-Loop Dynamic Games for Affine Control Systems," Springer Books, in: Alain Haurie & Georges Zaccour (ed.), Dynamic Games: Theory and Applications, chapter 0, pages 37-55, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-24602-4_2
    DOI: 10.1007/0-387-24602-9_2
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    Cited by:

    1. A. B. Malinowska & D. F. M. Torres, 2010. "The Hahn Quantum Variational Calculus," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 419-442, December.
    2. D. F. M. Torres & G. Leitmann, 2008. "Contrasting Two Transformation-based Methods for Obtaining Absolute Extrema," Journal of Optimization Theory and Applications, Springer, vol. 137(1), pages 53-59, April.

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