Node-consistent core for games played over event trees

We consider a class of dynamic games played over an event tree, where the players cooperate to optimize their expected joint payoff. Assuming that the players adopt the core as the solution concept of the cooperative game, we devise a node-decomposition of the imputations in the core such that each player finds it individually rational at each node to stick to cooperation rather than switching to a noncooperative strategy. We illustrate our approach with an example of pollution control.