This paper is a contribution to the literature which uses the theory of cooperative game in order to test the validity of the Coase Theorem in a 3-player game. We examine situations, not studied by Coase [1960], which give rise to new conditions under which the core of a 3-player game is (non)empty. Precisely, we put forward three main results. First, we demonstrate that the nonemptiness of the core depends on the liability rules and the allocation of rights. Second, we show that when the externality is non transferable, the core is nonempty if the polluter is not liable. We also establish that the core is always nonempty when negotiations between the polluter and the victims require unanimity. We provide a counterexample of the nonemptiness of the core in all other situations. Third, we show that, if the externality is non transferable, then an agent who does not negotiate can nevertheless influence the outcome of the negociation.