Groupe d’études et de recherche en analyse des décisions

Cooperation in differential game with coalitional structure

Ekaterina Gromova – Saint Petersburg State University, Russie

We consider an $$N$$-person differential game with a fixed coalitional structure. The cooperative game is described as a two-level construction. In the first level we consider a cooperative differential game in which coalitions act as players, aiming at maximizing their total payoff. The distribution of this payoff among coalitions is performed by computing the Shapley value on the base of classical (maxmin) superadditive characteristic function. In the second level of the game the components of the Shapley value obtained by coalitions are distributed among the members of coalitions. Here we also used the Shapley value as an optimality principle within the coalition, but implementing a new non-standard superadditive characteristic function. The described approach is illustrated by a 3-player differential game model of pollution control.