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Article

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

Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St. Petersburg, Russia
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Academic Editor: Vladimir Mazalov
Mathematics 2021, 9(7), 755; https://doi.org/10.3390/math9070755
Received: 21 February 2021 / Revised: 25 March 2021 / Accepted: 30 March 2021 / Published: 1 April 2021
(This article belongs to the Special Issue Mathematical Game Theory 2021)
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. View Full-Text
Keywords: differential game; network; cooperative game; strong time-consistent subcore; core; shapley value differential game; network; cooperative game; strong time-consistent subcore; core; shapley value
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MDPI and ACS Style

Tur, A.; Petrosyan, L. Strong Time-Consistent Solution for Cooperative Differential Games with Network Structure. Mathematics 2021, 9, 755. https://doi.org/10.3390/math9070755

AMA Style

Tur A, Petrosyan L. Strong Time-Consistent Solution for Cooperative Differential Games with Network Structure. Mathematics. 2021; 9(7):755. https://doi.org/10.3390/math9070755

Chicago/Turabian Style

Tur, Anna, and Leon Petrosyan. 2021. "Strong Time-Consistent Solution for Cooperative Differential Games with Network Structure" Mathematics 9, no. 7: 755. https://doi.org/10.3390/math9070755

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