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 (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.

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.

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.

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