A hybrid (differential-stochastic) zero-sum game with a fast stochastic part

Eitan Altman, Vladimir Gaitsgory

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contribution

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.
Original languageEnglish
Title of host publicationNew trends in dynamic games and applications
EditorsGJ Olsder
Place of PublicationBoston, MU
PublisherBirkhauser Boston
Pages47-59
Number of pages13
ISBN (Electronic)9781461242741
ISBN (Print)9781461287193
DOIs
Publication statusPublished - 1995
Externally publishedYes
Event6th International Symposium on Dynamic Games and Applications - ST JOVITE, Canada
Duration: 13 Jul 199415 Jul 1994

Publication series

NameANNALS OF THE INTERNATIONAL SOCIETY OF DYNAMIC GAMES
PublisherBIRKHAUSER BOSTON
Volume3

Conference

Conference6th International Symposium on Dynamic Games and Applications
CountryCanada
CityST JOVITE
Period13/07/9415/07/94

Keywords

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

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