Tractable classes of nonzero-sum open-loop Nash differential games: Theory and examples

1985 ◽  
Vol 45 (2) ◽  
pp. 179-197 ◽  
Author(s):  
E. Dockner ◽  
G. Feichtinger ◽  
S. J�rgensen
Keyword(s):  
Differential Games ◽  
Open Loop ◽  
Games Theory ◽  
Nash Differential Games

One-Player Differential Games

2017 ◽  
Author(s):  
João P. Hespanha
Keyword(s):  
Dynamical System ◽  
Differential Games ◽  
Continuous Time ◽  
Information Structure ◽  
Dynamic Games ◽  
State Feedback ◽  
Open Loop ◽  
Linear Quadratic ◽  
Time Dynamic ◽  
Termination Time

This chapter focuses on one-player continuous time dynamic games, that is, the optimal control of a continuous time dynamical system. It begins by considering a one-player continuous time differential game in which the (only) player wants to minimize either using an open-loop policy or a state-feedback policy. It then discusses continuous time cost-to-go, with the following conclusion: regardless of the information structure considered (open loop, state feedback, or other), it is not possible to obtain a cost lower than cost-to-go. It also explores continuous time dynamic programming, linear quadratic dynamic games, and differential games with variable termination time before concluding with a practice exercise and the corresponding solution.

Minimax methods for open-loop equilibria in N-person differential games. Part I: Linear quadratic games and constrained games

1986 ◽  
Vol 103 (1-2) ◽  
pp. 15-34
Author(s):  
Goong Chen ◽  
Quan Zheng ◽  
Jian-Xin Zhou
Keyword(s):  
Differential Games ◽  
Compact Convex ◽  
Dimensional Subspace ◽  
Open Loop ◽  
Finite Dimensional Subspace ◽  
Convex Constraints ◽  
Linear Quadratic ◽  
Matrix Games ◽  
Minimax Methods ◽  
Linear Quadratic Games

SynopsisIn [13], Nikaido and Isoda generalised von Neumann's symmetrisation method for matrix games. They showed that N-person noncooperative games can be treated by a minimax method.We apply this method to N-person differential games. Lukes and Russell [11] first studied N-person nonzero sum linear quadratic games in 1971. Here we have reproduced and strengthened their results. The existence and uniqueness of equilibria are completely determined by the invertibility of the decision operator, and the nonuniqueness of equilibrium strategies is only up to a finite dimensional subspace of the space of all admissible strategies.In the constrained case, we have established an existence result for games with a much weaker convexity assumption subject to compact convex constraints. We have also derived certain results for games with noncompact constraints. Several examples of quadratic and non-quadratic games are given to illustrate the theorem.Numerical computations are also possible and are given in the sequel [3].

scholarly journals Comparing Open-loop With Markov Equilibria in a Class of Differential Games

1999 ◽  
Vol 50 (4) ◽  
pp. 457-469 ◽  
Author(s):  
Ngo Van Long ◽  
Koji Shimomura ◽  
Harutaka Takahashi
Keyword(s):  
Differential Games ◽  
Open Loop ◽  
Markov Equilibria

Open Loop Approximation of Differential Games

1973 ◽  
Vol 11 (1) ◽  
pp. 20-31 ◽  
Author(s):  
Ronald J. Stern
Keyword(s):  
Differential Games ◽  
Open Loop ◽  
Loop Approximation
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