Cooperative differential games on networks

In modern literature on game theory one can find a number of papers concerning network games or games on networks. There are also some papers devoted to network games in dynamics. But it is necessary to mention that the cases under consideration did not use all possibilities which give the use of networks in game theoretical modeling for simplification of solutions in games. In this paper the new approaches are proposed which essentially simplify the solution of corresponding games. It is assumed that the payoff of player depends only upon action of players immediately connected with him through the given network. The new classes of strategies are introduced. These strategies include the possibility of cutting the link with neighboring payers during the game dependent from current state of the game. This gives the possibility of effective construction of Nash equilibrium and such important element of cooperative theory as characteristic function.