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Optimal Play in a Stochastic Differential Game
SIAM Journal on Control and Optimization, 1981This paper considers play in a two-person zero-sum differential game where the dynamics are given by a differential equation with additive white noise. Feedback strategies are employed. Standard results from control theory show that the maximizing player has an optimal response to any pre-announced strategy of the minimizing player.
Elliott, R. J., Davis, M. H. A.
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2014
In this chapter, we will deal with zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games, via the dynamic programming principle.In Sect. 4.1, we are concerned with basic concepts and definitions and we introduce stochastic differential games, referring to (Controlled ...
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In this chapter, we will deal with zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games, via the dynamic programming principle.In Sect. 4.1, we are concerned with basic concepts and definitions and we introduce stochastic differential games, referring to (Controlled ...
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Stochastic multi‐player pursuit–evasion differential games
International Journal of Robust and Nonlinear Control, 2007AbstractAutonomous aerial vehicles play an important role in military applications such as in search, surveillance and reconnaissance. Multi‐player stochastic pursuit–evasion (PE) differential game is a natural model for such operations involving intelligent moving targets with uncertainties.
Li, Dongxu +2 more
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Stochastic differential game in high frequency market
Automatica, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Saito, Taiga, Takahashi, Akihiko
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Zero-Sum Risk-Sensitive Stochastic Differential Games
Mathematics of Operations Research, 2012We study zero-sum risk-sensitive stochastic differential games on the infinite horizon with discounted and ergodic payoff criteria. Under certain assumptions, we establish the existence of values and saddle-point equilibria. We obtain our results by studying the corresponding Hamilton–Jacobi–Isaacs equations.
Basu, Arnab, Ghosh, Mrinal K
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Stochastic Differential Mean Field Games
2018The goal of this chapter is to propose solutions to asymptotic forms of the search for Nash equilibria for large stochastic differential games with mean field interactions. We implement the Mean Field Game strategy, initially developed by Lasry and Lions in an analytic set-up, in a purely probabilistic framework.
René Carmona, François Delarue
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An approach-evasion differential game: Stochastic guide
Proceedings of the Steklov Institute of Mathematics, 2010The differential equation \[ \dot{x}=f(t,x,u,v), t_{0}\leq t\leq \vartheta, u\in P, v\in Q, \] is approached by a positional differential game. The time \(\vartheta\) of the motion \(x[t],t_{0}\leq t\leq \vartheta\) belongs to a set \(M\) inside a set N and the evasion up to the time \(\vartheta\) of the motion \(x[t],t_{0}\leq t\leq \vartheta ...
Krasovskii, N. N., Kotel'nikova, A. N.
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Deterministic and Stochastic Differential Games
2016This chapter introduces the theory of deterministic and stochastic differential games, including the dynamic optimization techniques, (stochastic) differential games and their solution concepts, which will lay a foundation for later study.
Cheng-ke Zhang +3 more
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Risk-Sensitive Mean-Field Stochastic Differential Games
IFAC Proceedings Volumes, 2011In this paper, we study a class of risk-sensitive mean-field stochastic di fferential games. Under regularity assumptions, we use results from standard risk-sensitive di fferential game theory to show that the mean- field value of the exponentiated cost functional coincides with the value function of a Hamilton-Jacobi-Bellman-Fleming (HJBF) equation ...
Tembine, Hamidou +2 more
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On a problem of stochastic differential games
Journal of Optimization Theory and Applications, 1976The process of bargaining between management and union during a strike is modelled by a nonlinear stochastic differential game. It is assumed that the two sides bargain in the mood of a cooperative game. A pair of Pareto-optimal strategies is obtained.
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