Stackelberg Solutions of Feedback Type for Differential Games with Random Initial Data

Alberto Bressan () and Deling Wei ()

Dynamic Games and Applications, 2013, vol. 3, issue 3, 358 pages

Abstract: The paper is concerned with Stackelberg solutions for a differential game with deterministic dynamics but random initial data, where the leading player can adopt a strategy in feedback form: u 1 =u 1 (t,x). The first main result provides the existence of a Stackelberg equilibrium solution, assuming that the family of feedback controls u 1 (t,⋅) available to the leading player are constrained to a finite dimensional space. A second theorem provides necessary conditions for the optimality of a feedback strategy. Finally, in the case where the feedback u 1 is allowed to be an arbitrary function, an example illustrates a wide class of systems where the minimal cost for the leading player corresponds to an impulsive dynamics. In this case, a Stackelberg equilibrium solution does not exist, but a minimizing sequence of strategies can be described. Copyright Springer Science+Business Media New York 2013

Keywords: Differential game; Stackelberg equilibrium solution; Closed loop strategy (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s13235-012-0063-6

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