About one multistage non-antagonistic network game

In the paper, a multi-step non-antagonistic game is considered. The game has a finite number of stages, at the first stage a network is formed by simultaneously choosing communication vectors, and at the next, there are simultaneous non-antagonistic games, the payoffs in which depend on the controls chosen in the previous stage, as well as the behavior in the current stage. Players, at all stages except the first, have the opportunity to modify the network by removing any of their connections. A characteristic function is constructed for the model in a new way based on the calculation of optimal controls. For the case of a one-stage subgame, the supermodularity of the characteristic function is proved. As a solution, the Shapley value is considered, a simplification of the formula for calculating the components of the Shapley value for this characteristic function is given. Also, as a solution, a subset of the core (PRD-core) is considered. Strong dynamic stability has been proved for it. Work is illustrated by an example.