A Qualitative Characterization of Symmetric Open-Loop Nash Equilibria in Discounted Infinite Horizon Differential Games

2011 ◽  
Vol 149 (1) ◽  
pp. 151-174 ◽  
Author(s):  
C. Ling ◽  
M. R. Caputo
Keyword(s):  
Differential Games ◽  
Nash Equilibria ◽  
Infinite Horizon ◽  
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 Stochastic differential games with inside information

2016 ◽  
Vol 19 (03) ◽  
pp. 1650016 ◽  
Author(s):  
Olfa Draouil ◽  
Bernt Øksendal
Keyword(s):  
White Noise ◽  
Differential Games ◽  
Malliavin Calculus ◽  
Model Uncertainty ◽  
Nash Equilibria ◽  
Stochastic Calculus ◽  
Stochastic Differential Games ◽  
Inside Information ◽  
Jump Diffusions

We study stochastic differential games of jump diffusions, where the players have access to inside information. Our approach is based on anticipative stochastic calculus, white noise, Hida–Malliavin calculus, forward integrals and the Donsker delta functional. We obtain a characterization of Nash equilibria of such games in terms of the corresponding Hamiltonians. This is used to study applications to insider games in finance, specifically optimal insider consumption and optimal insider portfolio under model uncertainty.

scholarly journals Feedback and open-loop Nash equilibria in a class of differential games with random duration

2020 ◽  
Vol 13 ◽  
pp. 415-426
Author(s):  
Anna V. Tur ◽  
◽  
Natalya G. Magnitskaya ◽  
Keyword(s):  
Differential Games ◽  
Nash Equilibria ◽  
Finite Interval ◽  
Random Variable ◽  
Open Loop ◽  
Interval Methods

One class of differential games with random duration is considered. It is assumed that duration of the game is a random variable with values from a given finite interval. The game can be interrupted only on this interval. Methods of construction feedback and open-loop Nash equilibria for such games are proposed.

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