### 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,{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 language | English (US) |
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Pages (from-to) | 341-358 |

Number of pages | 18 |

Journal | Dynamic Games and Applications |

Volume | 3 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1 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