Weak Solutions of Mean-Field Stochastic Differential Equations and Application to Zero-Sum Stochastic Differential Games

2016 ◽  
Vol 54 (3) ◽  
pp. 1826-1858 ◽  
Author(s):  
Juan Li ◽  
Hui Min
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Differential Games ◽  
Weak Solutions ◽  
Mean Field ◽  
Stochastic Differential Games ◽  
Zero Sum

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.

Nash Equilibrium Payoffs for Stochastic Differential Games with two Reflecting Barriers

2015 ◽  
Vol 47 (02) ◽  
pp. 355-377
Author(s):  
Qian Lin
Keyword(s):  
Nash Equilibrium ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Differential Games ◽  
Backward Stochastic Differential Equations ◽  
Stochastic Differential Games ◽  
Cost Functionals ◽  
Reflecting Barriers

In this paper we study Nash equilibrium payoffs for nonzero-sum stochastic differential games with two reflecting barriers. We obtain an existence and a characterization of Nash equilibrium payoffs for nonzero-sum stochastic differential games with nonlinear cost functionals defined by doubly controlled reflected backward stochastic differential equations with two reflecting barriers.

scholarly journals Nash equilibria for nonzero-sum ergodic stochastic differential games

2017 ◽  
Vol 54 (4) ◽  
pp. 977-994 ◽  
Author(s):  
Samuel N. Cohen ◽  
Victor Fedyashov
Keyword(s):  
Nash Equilibrium ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Differential Games ◽  
Nash Equilibria ◽  
Backward Stochastic Differential Equations ◽  
Stochastic Differential Games ◽  
Ergodic Behaviour

Abstract We consider nonzero-sum games where multiple players control the drift of a process, and their payoffs depend on its ergodic behaviour. We establish their connection with systems of ergodic backward stochastic differential equations, and prove the existence of a Nash equilibrium under generalised Isaac's conditions. We also study the case of interacting players of different type.

Nash Equilibrium Payoffs for Stochastic Differential Games with two Reflecting Barriers

2015 ◽  
Vol 47 (2) ◽  
pp. 355-377 ◽  
Author(s):  
Qian Lin
Keyword(s):  
Nash Equilibrium ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Differential Games ◽  
Backward Stochastic Differential Equations ◽  
Stochastic Differential Games ◽  
Cost Functionals ◽  
Reflecting Barriers

In this paper we study Nash equilibrium payoffs for nonzero-sum stochastic differential games with two reflecting barriers. We obtain an existence and a characterization of Nash equilibrium payoffs for nonzero-sum stochastic differential games with nonlinear cost functionals defined by doubly controlled reflected backward stochastic differential equations with two reflecting barriers.

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