Stable agreements through liability rules: A multi-choice game approach to the social cost problem

We consider a class of social cost problems in which one polluter interacts with an arbitrary number of potential victims. Agents are supposed to cooperate and negotiate an optimal pollution level together with monetary transfers. We examine multi-choice cooperative games associated with a social cost problem and an assignment (or mapping) of rights. We introduce a class of mappings of rights that takes into account the pollution intensity and we consider three properties on mappings of rights: core compatibility, Kaldor–Hicks core compatibility and no veto power for a victim. We show that there exist only two families of mappings of rights that satisfy core compatibility, while no mapping of rights satisfies Kaldor–Hicks core compatibility and no veto power for a victim.