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

Alberto Bressan, Deling Wei

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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,{dot operator}) 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.

Original languageEnglish (US)
Pages (from-to)341-358
Number of pages18
JournalDynamic Games and Applications
Issue number3
StatePublished - Sep 2013

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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