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

Dean A. Carlson and George Leitmann

Chapter Chapter 2 in Dynamic Games: Theory and Applications, 2005, pp 37-55 from Springer

Abstract: 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

Keywords: Nash Equilibrium; Dynamic Game; Admissible Pair; Original Game; Strategy Pair (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/0-387-24602-9_2

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