Time-consistent Shapley value for games played over event trees

In this paper, we provide a decomposition over time of Shapley value for dynamic stochastic discrete-time games, where the uncertainty is described by an event tree. We show that the suggested dynamic allocation is time consistent, that is, along the cooperative state trajectory, no player has an incentive to switch to his noncooperative strategy. This property insures that the cooperative agreement is sustainable till its maturity. The considered class of games constitutes a natural paradigm to study dynamic competition in oligopolistic markets characterized by stochastic demand.