About the instability of cooperative communication structures in differential network games

In the paper, a cooperative differential network game is considered. We suppose that players simultaneously and independently choose the neighbor with whom they intend to interact during the game. Each player can choose neighbors from a fixed subset of players. Such subsets can be different for different players, and for each player, the number of its possible neighbors is limited. The players create the network to miximize the joint payoff. But network which is optimal at the initial time instant may cease to be so afterwords. As solution the Shapley value is proposed. The results are illustrated on an example.