Structures of Stochastic Differential Games for Which the Open-Loop Equilibrium Is Subgame Perfect

2016 ◽  
Author(s):  
Ricardo Josa-Fombellida ◽  
Juan P Rincon-Zapatero
Keyword(s):  
Differential Games ◽  
Stochastic Differential Games ◽  
Open Loop

Stochastic Differential Games for Which the Open-Loop Equilibrium is Subgame Perfect

2017 ◽  
Vol 8 (2) ◽  
pp. 379-400
Author(s):  
Ricardo Josa-Fombellida ◽  
Juan Pablo Rincón-Zapatero
Keyword(s):  
Differential Games ◽  
Stochastic Differential Games ◽  
Open Loop

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 Mean-field backward–forward stochastic differential equations and nonzero sum stochastic differential games

2020 ◽  
pp. 2150036
Author(s):  
Yinggu Chen ◽  
Boualem Djehiche ◽  
Said Hamadène
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Differential Games ◽  
Mean Field ◽  
Stochastic Differential Games ◽  
Open Loop ◽  
Random Coefficients ◽  
Linear Quadratic ◽  
Uniqueness Results ◽  
Weak Monotonicity

We study a general class of fully coupled backward–forward stochastic differential equations of mean-field type (MF-BFSDE). We derive existence and uniqueness results for such a system under weak monotonicity assumptions and without the non-degeneracy condition on the forward equation. This is achieved by suggesting an implicit approximation scheme that is shown to converge to the solution of the system of MF-BFSDE. We apply these results to derive an explicit form of open-loop Nash equilibrium strategies for nonzero sum mean-field linear-quadratic stochastic differential games with random coefficients. These strategies are valid for any time horizon of the game.

Bias and Overtaking Equilibria for Zero-Sum Stochastic Differential Games

2011 ◽  
Vol 153 (3) ◽  
pp. 662-687 ◽  
Author(s):  
Beatris Escobedo-Trujillo ◽  
Daniel López-Barrientos ◽  
Onésimo Hernández-Lerma
Keyword(s):  
Differential Games ◽  
Stochastic Differential Games ◽  
Zero Sum
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