In this paper, a dynamic theory for the kernel of n-person games given by Billera is studied. In terms of the (bargaining) trajectories associated with a game (i.e. solutions to the differential equations defined by the theory), an equivalence relation is defined. The "consistency" of these equivalence classes is examined. Then, viewing the pre-kernel as the set of equilibrium points of this system of differential equations, some topological, geometric, symmetry and stability properties of the pre-kernel are given. © 1977 Physica-Verlag.