This paper discusses games where cooperation is restricted by a hierarchical structure. The model assumes that there is a hierarchy between certain coalitions given by a partition. Face games (González-Díaz and Sánchez-Rodríguez in Games Econ Behav 62:100–105, 2008) play a central role in the definition of the proposed hierarchical game. It turns out that the Shapley value of the hierarchical game coincides with the Faigle and Kern precedence constraint value (Faigle and Kern in Int J Game Theory 21:249–266, 1992) and with some particular weighted Shapley value (Kalai and Samet in Int J Game Theory 16:205–222, 1987). Two new characterizations of this hierarchical value are given. Finally, an application of the model is given for bankruptcy problems.