Cooperative Optimality Principles in Differential Games on Networks

2021 ◽  
Vol 82 (6) ◽  
pp. 1095-1106
Author(s):  
A. V. Tur ◽  
L. A. Petrosyan
Keyword(s):  
Differential Games ◽  
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 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.

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