An example of two level cooperation for Differential Game with Pairwise Interactions in pollution control problems

Yang He, Leon A. Petrosyan

Saint Petersburg State University, Faculty of Applied Mathematics and Control Processes

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 pollution control problem involving pairwise interactions.

Keywords: cooperative games, differential network games, pairwise interactions, Shapley value.

UDC: 519.83, 004.42
BBK: 22.18

Received: 21.11.2024
Revised: 01.04.2025
Accepted: 19.06.2025