Correlated Equilibria for Infinite Horizon Nonzero-Sum Stochastic Differential Games

2019 ◽  
pp. 181-200
Author(s):  
Beatris A. Escobedo-Trujillo ◽  
Héctor Jasso-Fuentes
Keyword(s):  
Differential Games ◽  
Infinite Horizon ◽  
Stochastic Differential Games ◽  
Correlated Equilibria

Infinite-horizon non-zero-sum stochastic differential games with additive structure

2015 ◽  
pp. dnv045
Author(s):  
Héctor Jasso-Fuentes ◽  
José Daniel López-Barrientos ◽  
Beatris Adriana Escobedo-Trujillo
Keyword(s):  
Differential Games ◽  
Infinite Horizon ◽  
Stochastic Differential Games ◽  
Additive Structure ◽  
Zero Sum

scholarly journals Mean-field linear-quadratic stochastic differential games in an infinite horizon

2021 ◽  
Author(s):  
Xun Li ◽  
Jingtao Shi ◽  
Jiongmin Yong
Keyword(s):  
Nash Equilibrium ◽  
Differential Games ◽  
Closed Loop ◽  
Infinite Horizon ◽  
Mean Field ◽  
Riccati Equations ◽  
Stochastic Differential Games ◽  
Open Loop ◽  
Linear Quadratic ◽  
Algebraic Riccati Equations

This paper is concerned with two-person mean-field linear-quadratic non-zero sum stochastic differential games in an infinite horizon. Both open-loop and closed-loop Nash equilibria are introduced. Existence of an open-loop Nash equilibrium is characterized by the solvability of a system of mean-field forward-backward stochastic differential equations in an infinite horizon and the convexity of the cost functionals, and the closed-loop representation of an open-loop Nash equilibrium is given through the solution to a system of two coupled non-symmetric algebraic Riccati equations. The existence of a closed-loop Nash equilibrium is  characterized by the solvability of a system of two coupled symmetric algebraic Riccati equations. Two-person mean-field linear-quadratic zero-sum stochastic differential games in an infinite time horizon are also considered. Both the existence of open-loop and closed-loop saddle points are characterized by the solvability of a system of two coupled generalized algebraic Riccati equations with static stabilizing solutions. Mean-field linear-quadratic stochastic optimal control problems in an infinite horizon are discussed as well, for which it is proved that the open-loop solvability and closed-loop solvability are equivalent.

scholarly journals Stability and Linear Quadratic Differential Games of Discrete-Time Markovian Jump Linear Systems with State-Dependent Noise

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Huiying Sun ◽  
Meng Li ◽  
Shenglin Ji ◽  
Long Yan
Keyword(s):  
Linear Systems ◽  
Differential Games ◽  
Discrete Time ◽  
Infinite Horizon ◽  
Stochastic Differential Games ◽  
Markovian Jump ◽  
Linear Quadratic ◽  
Jump Linear Systems ◽  
State Dependent ◽  
Markovian Jump Linear Systems

We mainly consider the stability of discrete-time Markovian jump linear systems with state-dependent noise as well as its linear quadratic (LQ) differential games. A necessary and sufficient condition involved with the connection between stochasticTn-stability of Markovian jump linear systems with state-dependent noise and Lyapunov equation is proposed. And using the theory of stochasticTn-stability, we give the optimal strategies and the optimal cost values for infinite horizon LQ stochastic differential games. It is demonstrated that the solutions of infinite horizon LQ stochastic differential games are concerned with four coupled generalized algebraic Riccati equations (GAREs). Finally, an iterative algorithm is presented to solve the four coupled GAREs and a simulation example is given to illustrate the effectiveness of it.

scholarly journals Infinite Horizon LQ Zero-Sum Stochastic Differential Games with Markovian Jumps

2012 ◽  
Vol 03 (10) ◽  
pp. 1321-1326 ◽  
Author(s):  
Huai-Nian Zhu ◽  
Cheng-Ke Zhang ◽  
Ning Bin
Keyword(s):  
Differential Games ◽  
Infinite Horizon ◽  
Stochastic Differential Games ◽  
Zero Sum

Near Optimal Strategy for Nonlinear Stochastic Differential Games Based on the Technique of Statistical Linearization

2014 ◽  
Vol 39 (4) ◽  
pp. 390-399
Author(s):  
Ping ZHANG ◽  
Yang-Wang FANG ◽  
Xiao-Bin HUI ◽  
Xin-Ai LIU ◽  
Liang LI
Keyword(s):  
Differential Games ◽  
Optimal Strategy ◽  
Stochastic Differential Games ◽  
Statistical Linearization
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