MSC: 91A23, 91A12, 91A43
DOI: 10.21538/0134-4889-2021-27-3-286-295
Full text
In the paper, the differential games on networks with partner sets are considered. The payoffs of a given player depend on his actions and the actions of the players from his partner set. The cooperative version of the game is proposed, and the special type of characteristic function is introduced. It is proved the constructed cooperative game is convex. Using the properties of the payoff functions and the constructed characteristic function, the Shapley Value and $\tau$-value are computed. It is also proved that in this special class of differential games the Shapley value is time-consistent.
Keywords: Shapley value, differential network game, time consistency, partner sets
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Received May 31, 2021
Revised June 15, 2021
Accepted August 2, 2021
Funding Agency: The first author is supported by Russian Science Foundation, the grant ``Optimal Behavior in Conflict-Controlled Systems'' (project no. 17-11-01079).
Leon Aganesovich Petrosyan, Dr. Phys.-Math. Sci., Prof., Saint Petersburg State University, St. Petersburg, 199034 Russia, e-mail: l.petrosyan@spbu.ru
David W.K. Yeung, Prof. Dr. Dr.h.c., Hong Kong Shue Yan University, Hong Kong, China, e-mail: dwkyeung@hksyu.edu
Yaroslavna Borisovna Pankratova, Cand. Sci. (Phys.-Math.), Saint Petersburg University, St. Petersburg, 199034 Russia, e-mail: y.pankratova@spbu.ru
Cite this article as: L.A. Petrosyan, D. Yeung, Y.B. Pankratоva. Cooperative Differential Games with Partner Sets on Networks. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2021, vol. 27, no. 3, pp. 286–295.
Русский
Л.А. Петросян, Д. Янг, Я.Б. Панкратова. Кооперативные дифференциальные игры с партнерскими множествами на сетях
Рассматриваются сетевые дифференциальные игры с партнерскими множествами. Выигрыш каждого игрока зависит от его действий и действий игроков из его партнерского множества. В статье предложена кооперативная версия игры и введен особый тип характеристической функции. Доказано, что построенная кооперативная игра является выпуклой. Свойства функций выигрыша и построенной характеристической функции используются для вычисления вектора Шепли и $\tau$-вектора. Также доказано, что в указанном классе дифференциальных игр вектор Шепли динамически устойчив.
Ключевые слова: вектор Шепли, сетевая дифференциальная игра, динамическая устойчивость, партнерские множества
