scholarly journals Sub- and Super-optimality Principles and Construction of Almost Optimal Strategies for Differential Games in Hilbert Spaces

2010 ◽  
pp. 149-163
Author(s):  
Andrzej Świȩch
Keyword(s):  
Differential Games ◽  
Hilbert Spaces ◽  
Optimal Strategies ◽  
Optimality Principles

scholarly journals Cooperative optimality principals in differential games on networks

2020 ◽  
Vol 12 (4) ◽  
pp. 93-111
Author(s):  
Анна Тур ◽  
Anna Tur ◽  
Леон Аганесович Петросян ◽  
Leon Petrosyan
Keyword(s):  
Characteristic Function ◽  
Differential Games ◽  
Network Structure ◽  
Shapley Value ◽  
The Core ◽  
Investment Game ◽  
The Shapley Value ◽  
Research Investment ◽  
Optimality Principles

The paper describes a class of differential games on networks. The construction of cooperative optimality principles using a special type of characteristic function that takes into account the network structure of the game is investigated. The core, the Shapley value and the tau-value are used as cooperative optimality principles. The results are demonstrated on a model of a differential research investment game, where the Shapley value and the tau-value are explicitly constructed.

scholarly journals Syntheses of differential games and pseudo-Riccati equations

2002 ◽  
Vol 7 (2) ◽  
pp. 61-83 ◽  
Author(s):  
Yuncheng You
Keyword(s):  
Dynamical Systems ◽  
Saddle Point ◽  
Riccati Equation ◽  
Differential Games ◽  
Regular Solution ◽  
Closed Loop ◽  
Optimal Strategies ◽  
Time Parameter ◽  
Fixed Duration ◽  
Linear Dynamical Systems

For differential games of fixed duration of linear dynamical systems with nonquadratic payoff functionals, it is proved that the value and the optimal strategies as saddle point exist whenever the associated pseudo-Riccati equation has a regular solutionP(t,x). Then the closed-loop optimal strategies are given byu(t)=−R−1B∗P(t,x(t)), v(t)=−S−1C∗P(t,x(t)). For differential game problems of Mayer type, the existence of a regular solution to the pseudo-Riccati equation is proved under certain assumptions and a constructive expression of that solution can be found by solving an algebraic equation with time parameter.

scholarly journals Cooperative differential game model with continuous updating

2020 ◽  
Vol 12 (2) ◽  
pp. 82-109
Author(s):  
Ованес Леонович Петросян ◽  
Ovanes Petrosian ◽  
Анна Викторовна Тур ◽  
Anna Tur ◽  
Цзэян Ван ◽  
...  
Keyword(s):  
Differential Games ◽  
Optimal Strategies ◽  
Limited Resource ◽  
Game Model ◽  
Cooperative Solution ◽  
Cooperative Strategies ◽  
The Moment ◽  
Resource Extraction Game ◽  
Cooperative Differential Game ◽  
Cooperative Differential Games

The paper considers and describes the class of cooperative differential games with continuous updating. Such a class of differential games is new, at the moment only the classnoncooperative game models with continuous updating have been studied. This paper describes the process of constructing cooperative strategies, cooperative trajectory, characteristicfunction and cooperative solution with continuous updating. Cooperative case of limited resource extraction game model with continuous updating is considered. Optimal strategies,characteristic function and cooperative solution are constructed. The Shapley vector is used as a cooperative solution. The numerical simulation results are demonstrated in the Matlabenvironment.

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