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This research aims to investigate cooperative differential games on hypergraphs by examining the properties of a characteristic function.

About One Differential Game on Hypergraph

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This research aims to investigate cooperative differential games on hypergraphs by examining the properties of a characteristic function.
Introduced a special type of characteristic function considering the hypergraph structure
Studied the properties of the proposed function
Utilized the Shapley value as an optimality principle
Derived an explicit formula for the Shapley value for cycle-free line graphs
Provided an illustrative example to demonstrate the concepts.
Formulated a characteristic function tailored for hypergraphs
Obtained an explicit formula for the Shapley value in specific scenarios
Demonstrated the application of the Shapley value in cooperative game settings.

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Cooperative game theory explores optimal strategies in hypergraphs, highlighting applications in network structures.

Tur et al. (2025) studied this question.

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