On a approach to the construction of characteristic function for cooperative differential games

The paper presents a novel approach to the construction of characteristic functions for cooperative differential games. The characteristic function of coalition $S$ is computed in two stages: first, optimal control strategies maximizing the total payoff of the players; next, the cooperative optimal strategies are used by the players from the coalition $S$ while the left-out players from $N \setminus S$ use the strategies minimizing the total payoff of the players from $S$. The characteristic function defined in this way is superadditive. In addition, it possesses a number of other useful properties. To illustrate this result we compute characteristic function for a specific differential game of pollution control.