Cooperative network games with a changing communication structure

The paper considers a cooperative differential network game. We assume that at the beginning of the game, players simultaneously and independently choose a 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 possible neighbors is fixed. Then, at given time instants, players have the opportunity to change the network. Players create a network to maximize their joint payoff. However, a network that is optimal at the initial time instant may later cease to be optimal. The C-core and the Shapley value are considered as a solution of the cooperative game.