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

IF 0.8 4区数学 Q3 MATHEMATICS

Doklady Mathematics Pub Date : 2026-04-16 DOI:10.1134/S1064562425601040

Y. He, L. A. Petrosyan

引用次数: 0

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.

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污染控制问题中具有两两相互作用的微分对策的两层合作例子

在本文中，我们考虑具有两两交互作用的微分对策中的两个层次的合作。在第一级，将伙伴集视为参与者，并使用Shapley值在伙伴集之间分配收益。在第二级，这种收益分配给每个伙伴集中的个体参与者。构造了一个新的特征函数，并证明了它的凸性。结果通过一个涉及两两相互作用的污染控制问题来说明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Doklady Mathematics 数学-数学

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

3-6 weeks

期刊介绍： Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.