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Abstract <p>In this paper, we consider two levels of cooperation in a differential game with pairwise interactions. At the first level, the partner sets are treated as players, and the Shapley value is used to allocate the payoff among the partner sets. At the second level, this payoff is distributed among the individual players within each partner set. A new characteristic function is constructed, and its convexity is proved. The results are illustrated through a pollution control problem involving pairwise interactions.</p>

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An Example of Two Level Cooperation for Differential Game with Pairwise Interactions in Pollution Control Problems

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Y. He,
  • L. A. Petrosyan

摘要

Abstract

In this paper, we consider two levels of cooperation in a differential game with pairwise interactions. At the first level, the partner sets are treated as players, and the Shapley value is used to allocate the payoff among the partner sets. At the second level, this payoff is distributed among the individual players within each partner set. A new characteristic function is constructed, and its convexity is proved. The results are illustrated through a pollution control problem involving pairwise interactions.