Zero-sum Markov games with stopping and impulsive strategies

Stettner, Łukasz

doi:10.1007/bf01460115

Cited by 67 publications

(62 citation statements)

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“…Here we have established the existence of a saddle point equilibrium. This problem has been studied by Stettner in [6] for a class of Markov processes using the semigroup formulation. Thus the result for this special case in Section 4 is subsumed by the corresponding results in [6].…”

Section: Discussionmentioning

confidence: 99%

“…This problem has been studied by Stettner in [6] for a class of Markov processes using the semigroup formulation. Thus the result for this special case in Section 4 is subsumed by the corresponding results in [6]. We have, however, used the method of viscosity solutions to arrive at the same result.…”

Section: Discussionmentioning

confidence: 99%

“…Differential games with controls alone have been studied extensively (see [1] and references therein). Stochastic games with stopping times are studied for a class of Markov processes in [6].…”

Section: Introductionmentioning

confidence: 99%

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Differential Games of Mixed Type with Control and Stopping Times

Ghosh¹,

Rao²,

Dharmatti³

2009

Nonlinear differ. equ. appl.

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Abstract. We study a zero sum differential game of mixed type where each player uses both control and stopping times. Under certain conditions we show that the value function for this problem exists and is the unique viscosity solution of the corresponding variational inequalities. We also show the existence of saddle point equilibrium for a special case of differential game. Mathematics Subject Classification (2000). 90D25, 90D26.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Differential Games of Mixed Type with Control and Stopping Times

Ghosh¹,

Rao²,

Dharmatti³

2009

Nonlinear differ. equ. appl.

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“…Recently, Ferenstein [51] solved the version of the nonzero-sum Dynkin's game with different, special, payoff structure. Continuous time version of such a game problem was studied by Bensoussan & Friedman [52], [53], Krylov [54], Bismut [55], Stettner [56], Lepeltier & Maingueneau [57] and many others.…”

Section: Stopping Gamesmentioning

confidence: 99%

Non-Zero-Sum Stochastic Games

Jaśkiewicz¹,

Nowak²

2017

Handbook of Dynamic Game Theory

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Abstract. This paper treats stochastic games. A nonzero-sum average payoff stochastic games with arbitrary state spaces and the stopping games are considered. Such models of games very well fit in some studies in economic theory and operations research. A correlation of strategies of the players, involving "public signals", is allowed in the nonzero-sum average payoff stochastic games. The main result is an extension of the correlated equilibrium theorem proved recently by Nowak and Raghavan for dynamic games with discounting to the average payoff stochastic games. The stopping games are special model of stochastic games. The version of Dynkin's game related to observation of Markov process with random priority assignment mechanism of states is presented in the paper. The zero-sum and nonzero-sum games are considered. The paper also provides a brief overview of the theory of nonzero-sum stochastic games and stopping games which are very far from being complete.

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“…In other words, each player has the option of not stopping the game at any time. We refer to [7] for a similar treatment to stochastic games with stopping times. We now define the lower and upper value functions.…”

Section: Application To Stochastic Gamesmentioning

confidence: 99%