scholarly journals ε-Nash equilibrium in stochastic differential games with mean-field interaction and controlled jumps

2019 ◽  
Vol 154 ◽  
pp. 108522
Author(s):  
Chiara Benazzoli ◽  
Luciano Campi ◽  
Luca Di Persio
Keyword(s):  
Nash Equilibrium ◽  
Differential Games ◽  
Mean Field ◽  
Stochastic Differential Games ◽  
Field Interaction

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.

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.

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