scholarly journals A substitute for the classical Neumann–Morgenstern characteristic function in cooperative differential games

2020 ◽  
Vol 7 (2) ◽  
pp. 105-122
Author(s):  
Ekaterina Gromova ◽  
◽  
Ekaterina Marova ◽  
Dmitry Gromov
Keyword(s):  
Characteristic Function ◽  
Differential Games ◽  
Cooperative Differential Games

scholarly journals Feedback based strategies for autonomous linear quadratic cooperative differential games with continuous updating

2020 ◽  
Vol 13 ◽  
pp. 244-251
Author(s):  
Ildus Kuchkarov ◽  
Keyword(s):  
Characteristic Function ◽  
Differential Games ◽  
Shapley Value ◽  
Linear Quadratic ◽  
Cooperative Solution ◽  
Cooperative Strategies ◽  
The Shapley Value ◽  
Cooperative Differential Games

In the paper the class of linear quadratic cooperative differential games with continuous updating is considered. Here the case of feedback based strategies is used to construct cooperative strategies with continuous updating. Characteristic function with continuous updating, cooperative trajectory with continuous updating and cooperative solution are constructed. For the cooperative solution we use the Shapley value.

scholarly journals Superadditive extension of characteristic functions for cooperative differential games

2020 ◽  
Vol 12 (4) ◽  
pp. 40-61
Author(s):  
Екатерина Викторовна Громова ◽  
Ekaterina Gromova ◽  
Екатерина Марова ◽  
Ekaterina Marova
Keyword(s):  
Characteristic Function ◽  
Differential Games ◽  
Differential Game ◽  
Characteristic Functions ◽  
Cooperative Differential Games

The paper provides a constructive theorem that allows one to construct a superadditive characteristic function in a differential game based on a non-superadditive one. As an example, a differential game is considered in which the delta - and eta - characteristic functions are not superadditive. An additional construction is carried out and it is shown that the obtained functions satisfy superadditivity  

scholarly journals Strong Time-Consistent Solution for Cooperative Differential Games with Network Structure

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 755
Author(s):  
Anna Tur ◽  
Leon Petrosyan
Keyword(s):  
Characteristic Function ◽  
Differential Games ◽  
Network Structure ◽  
Shapley Value ◽  
Explicit Calculation ◽  
The Shapley Value ◽  
Consistent Solution ◽  
Optimality Principles ◽  
Cooperative Differential Games

One class of cooperative differential games on networks is considered. It is assumed that interaction on the network is possible not only between neighboring players, but also between players connected by paths. Various cooperative optimality principles and their properties for such games are investigated. The construction of the characteristic function is proposed, taking into account the network structure of the game and the ability of players to cut off connections. The conditions under which a strong time-consistent subcore is not empty are studied. The formula for explicit calculation of the Shapley value is derived. The results are illustrated by the example of one differential marketing game.

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.

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