On stochastic hybrid zero-sum games with nonlinear slow dynamics

Minh Tuan Nguyen, Eitan Altman, Vladimir Gaitsgory

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

Abstract

This paper considers a continuous-time stochastic hybrid system, controlled by two players with opposite objectives (zero-sum game). The parameters of the system may jump at discrete moments of time according to a Markov decision process, namely, a Markov chain that is directly controlled by both players and has finite state and action spaces. Assuming that the length of the intervals between the jumps is defined by a small parameter epsilon, the value of this game is shown to have a limit as the small parameter tends to 0. This limit is established to coincide with the viscosity solution of some Hamilton-Jacobi-type equations.

Original languageEnglish
Title of host publicationAdvances in dynamic games and applications
EditorsEitan Altman, Odile Pourtallier
Place of PublicationBoston, MA
PublisherBirkhauser Boston
Pages129-145
Number of pages17
Volume6
ISBN (Electronic)9781461201557
ISBN (Print)9781461266372
DOIs
Publication statusPublished - 2001
Externally publishedYes
Event8th International Symposium of Dynamic Games and Applications - Maastricht, Netherlands
Duration: 5 Jul 19988 Jul 1998

Publication series

NameANNALS OF THE INTERNATIONAL SOCIETY OF DYNAMIC GAMES
PublisherBIRKHAUSER BOSTON
Volume6

Conference

Conference8th International Symposium of Dynamic Games and Applications
CountryNetherlands
CityMaastricht
Period5/07/988/07/98

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