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Abstract <p>A cooperative differential game on a hypergraph is considered. A characteristic function of special type is introduced taking into account the network structure of the game, and its properties are studied. The Shapley value is used as a cooperative optimality principle. For games on hypergraphs with a cycle-free line graph, an explicit formula for the Shapley value is obtained. An illustrative example is considered.</p>

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About One Differential Game on Hypergraph

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • A. V. Tur,
  • I. R. Tantlevskij

摘要

Abstract

A cooperative differential game on a hypergraph is considered. A characteristic function of special type is introduced taking into account the network structure of the game, and its properties are studied. The Shapley value is used as a cooperative optimality principle. For games on hypergraphs with a cycle-free line graph, an explicit formula for the Shapley value is obtained. An illustrative example is considered.