Solution of Differential Games with Network Structure in Marketing

Gromova, Ekaterina; Malakhova, Anastasiya

doi:10.1007/978-3-030-51941-4_4

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2021

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“…For example, a differential game of a duopoly with network externalities is examined in [5]. Differential games with network structure in marketing are considered in [6]. An application of such games in regional cooperation is developed in [7].…”

Section: Introductionmentioning

confidence: 99%

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

Tur

Petrosyan

2021

Mathematics

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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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Section: Introductionmentioning

confidence: 99%