## Abstract

We consider in this paper a continuous time stochastic hybrid system

with a finite time horizon, controlled by two players with opposite

objectives (zero-sum game). Player one wishes to maximize some linear

function of the expected state trajectory, and player two wishes to

minimize it. The state evolves according to a linear dynamic. The parameters

of the state evolution equation may change at discrete times

according to a MDP, i.e., a Markov chain that is directly controlled by

both players, and has a countable state space. Each player has a finite

action space. We use a procedure similar in form to the maximum

principle; this determines a pair of stationary strategies for the players,

which is asymptotically a saddle point, as the number of transitions

during the finite time horizon grows to infinity.

with a finite time horizon, controlled by two players with opposite

objectives (zero-sum game). Player one wishes to maximize some linear

function of the expected state trajectory, and player two wishes to

minimize it. The state evolves according to a linear dynamic. The parameters

of the state evolution equation may change at discrete times

according to a MDP, i.e., a Markov chain that is directly controlled by

both players, and has a countable state space. Each player has a finite

action space. We use a procedure similar in form to the maximum

principle; this determines a pair of stationary strategies for the players,

which is asymptotically a saddle point, as the number of transitions

during the finite time horizon grows to infinity.

Original language | English |
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Title of host publication | New trends in dynamic games and applications |

Editors | GJ Olsder |

Place of Publication | Boston, MU |

Publisher | Birkhauser Boston |

Pages | 47-59 |

Number of pages | 13 |

ISBN (Electronic) | 9781461242741 |

ISBN (Print) | 9781461287193 |

DOIs | |

Publication status | Published - 1995 |

Externally published | Yes |

Event | 6th International Symposium on Dynamic Games and Applications - ST JOVITE, Canada Duration: 13 Jul 1994 → 15 Jul 1994 |

### Publication series

Name | ANNALS OF THE INTERNATIONAL SOCIETY OF DYNAMIC GAMES |
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Publisher | BIRKHAUSER BOSTON |

Volume | 3 |

### Conference

Conference | 6th International Symposium on Dynamic Games and Applications |
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Country | Canada |

City | ST JOVITE |

Period | 13/07/94 → 15/07/94 |

## Keywords

- hybrid stochastic systems
- stochastic games
- asymptotic optimality
- linear dynamics
- Markov decision processes
- finite horizon