A class of differential games for which the closed-loop and open-loop Nash equilibria coincide

1982 ◽  
Vol 36 (2) ◽  
pp. 253-262 ◽  
Author(s):  
J. F. Reinganum
Keyword(s):  
Differential Games ◽  
Nash Equilibria ◽  
Closed Loop ◽  
Open Loop

scholarly journals Uncoupling Isaacs’equations in nonzero-sum two-player differential games : The example of conflict over parental care

2008 ◽  
Vol Volume 9, 2007 Conference in... ◽  
Author(s):  
Frédéric Hamelin ◽  
Pierre Bernhard
Keyword(s):  
Parental Care ◽  
Differential Games ◽  
Nash Equilibria ◽  
Closed Loop ◽  
Classical Problem ◽  
Complete Analysis ◽  
Behavioural Ecology ◽  
International Audience ◽  
Set Up

International audience We use a recently uncovered decoupling of Isaacs PDE’s of some mixed closed loop Nash equilibria to give a rather complete analysis of the classical problem of conflict over parental care in behavioural ecology, for a more general set up than had been considered heretofore. On utilise un découplage récemment mis en évidence des équations d’Isaacs d’un jeu différentiel pour des stratégies mixtes singulières particulières pour donner une analyse assez complète d’un problème classique en écologie comportementale concernant le conflit à propos des soins parentaux.

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 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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