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

Anna Tur and Leon Petrosyan
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Anna Tur: Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St. Petersburg, Russia
Leon Petrosyan: Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St. Petersburg, Russia

Mathematics, 2021, vol. 9, issue 7, 1-15

Abstract: 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.

Keywords: differential game; network; cooperative game; strong time-consistent subcore; core; shapley value (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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