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On a problem of stochastic differential games

Journal of Optimization Theory and Applications, 1976
The 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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Stochastic differential portfolio games

Journal of Applied Probability, 1998
We study stochastic dynamic investment games in continuous time between two investors (players) who have available two different, but possibly correlated, investment opportunities. There is a single payoff function which depends on both investors’ wealth processes.
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Optimal Play in a Stochastic Differential Game

SIAM Journal on Control and Optimization, 1981
This 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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Switching Games of Stochastic Differential Systems

SIAM Journal on Control and Optimization, 2007
A two-player, zero-sum, switching game is formulated for general stochastic differential systems and is studied using a combined dynamic programming and viscosity solution approach. The existence of the game value is proved. For the proof of the related dynamic programming principle (DDP) for the lower and upper value functions, the measurability ...
Tang, S, Hou, SH
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Numerical Approximations for Stochastic Differential Games

SIAM Journal on Control and Optimization, 2002
The Markov chain approximation method is a widely used, robust, relatively easy to use, and efficient family of methods for the bulk of stochastic control problems in continuous time for reflected-jump-diffusion-type models. It has been shown to converge under broad conditions, and there are good algorithms for solving the numerical problems if the ...
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Stochastic Differential Game Techniques

1981
The paper deals with the theory of stochastic differential games and includes a comprehensive review of the subject under discussion. The main aspects of stochastic differential games discussed in the paper are: problem formulation, solution concepts and the difficulties encountered in trying to obtain a solution.
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Linear Exponential Quadratic Stochastic Differential Games

IEEE Transactions on Automatic Control, 2016
In this technical note a two person noncooperative stochastic differential game described by a linear stochastic equation with a Brownian motion and a payoff that is the exponential of a quadratic functional in the state and the control strategies of the two players is explicitly solved. The optimal strategies form a Nash equilibrium.
Tyrone Duncan
exaly   +3 more sources

Transboundary Emission Under Stochastic Differential Game

International Game Theory Review, 2020
In this study we provide a more robust transboundary industrial pollution reduction strategy for global emission collaborations. We consider the dynamics of each country’s quantity of pollution as a Brownian motion with Jumps to capture the systematic jumps caused by surprise effects arising from policy uncertainties within the economy. When the output
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On a Differential Game in a Stochastic System

Proceedings of the Steklov Institute of Mathematics, 2020
We study the game problem of approach for a system whose dynamics is described by a stochastic differential equation in a Hilbert space. The main assumption on the equation is that the operator multiplying the system state generates a strongly continuous semigroup (a semigroup of class  $$C_{0}$$ ).
L. A. Vlasenko   +2 more
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Stochastic Differential Games

2019
In this section we present the dynamic programming approach to stochastic differential games. We only present the case for zero sum games. For the extension to non-zero sum games, we refer to [MO].
Bernt Øksendal, Agnès Sulem
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