On stochastic hybrid zero-sum games with nonlinear slow dynamics

Minh Tuan Nguyen; Eitan Altman; Vladimir Gaitsgory

doi:10.1007/978-1-4612-0155-7_9

On stochastic hybrid zero-sum games with nonlinear slow dynamics

Minh Tuan Nguyen, Eitan Altman, Vladimir Gaitsgory

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-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 language	English
Title of host publication	Advances in dynamic games and applications
Editors	Eitan Altman, Odile Pourtallier
Place of Publication	Boston, MA
Publisher	Birkhauser Boston
Pages	129-145
Number of pages	17
Volume	6
ISBN (Electronic)	9781461201557
ISBN (Print)	9781461266372
DOIs	https://doi.org/10.1007/978-1-4612-0155-7_9
Publication status	Published - 2001
Externally published	Yes
Event	8th International Symposium of Dynamic Games and Applications - Maastricht, Netherlands Duration: 5 Jul 1998 → 8 Jul 1998

Publication series

Name	ANNALS OF THE INTERNATIONAL SOCIETY OF DYNAMIC GAMES
Publisher	BIRKHAUSER BOSTON
Volume	6

Conference

Conference	8th International Symposium of Dynamic Games and Applications
Country	Netherlands
City	Maastricht
Period	5/07/98 → 8/07/98

Access to Document

10.1007/978-1-4612-0155-7_9

Cite this

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title = "On stochastic hybrid zero-sum games with nonlinear slow dynamics",

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.",

author = "Nguyen, {Minh Tuan} and Eitan Altman and Vladimir Gaitsgory",

year = "2001",

doi = "10.1007/978-1-4612-0155-7_9",

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editor = "Eitan Altman and Odile Pourtallier",

booktitle = "Advances in dynamic games and applications",

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note = "8th International Symposium of Dynamic Games and Applications ; Conference date: 05-07-1998 Through 08-07-1998",

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Nguyen, MT, Altman, E & Gaitsgory, V 2001, On stochastic hybrid zero-sum games with nonlinear slow dynamics. in E Altman & O Pourtallier (eds), Advances in dynamic games and applications. vol. 6, ANNALS OF THE INTERNATIONAL SOCIETY OF DYNAMIC GAMES, vol. 6, Birkhauser Boston, Boston, MA, pp. 129-145, 8th International Symposium of Dynamic Games and Applications, Maastricht, Netherlands, 5/07/98. https://doi.org/10.1007/978-1-4612-0155-7_9

On stochastic hybrid zero-sum games with nonlinear slow dynamics. / Nguyen, Minh Tuan; Altman, Eitan; Gaitsgory, Vladimir.

Advances in dynamic games and applications. ed. / Eitan Altman; Odile Pourtallier. Vol. 6 Boston, MA : Birkhauser Boston, 2001. p. 129-145 (ANNALS OF THE INTERNATIONAL SOCIETY OF DYNAMIC GAMES; Vol. 6).

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

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AB - 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.

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