Two-level cooperation in coalitional differential games

We consider a differential game with prescribed duration and given coalitional partition of the set of players. The cooperative game proceeds in two stages. At the first stage the players (coalitions) maximize the total payoff and then distribute it according to the Shapley value. At the second stage the components of the Shapley value are distributed inside fixed coalitions. We study the time consistency of the proposed two-level cooperative solution. The problem is solved by means of an imputation distribution procedure. The results are illustrated by a differential game of emission reduction.