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.

我们考虑一类社会成本问题，其中一个污染者与任意数量的潜在受害者互动。代理商应与货币转移一起合作并商定最佳污染水平。我们研究与社会成本问题和权利的分配（或映射）相关的多项选择合作游戏。我们引入一类考虑了污染强度的权利映射，并考虑了权利映射的三个属性：核心兼容性，Kaldor-Hicks核心兼容性以及对受害者没有否决权。我们证明，只有两个满足核心兼容性的权利映射系列，而没有权利映射满足Kaldor-Hicks核心兼容性，并且没有对受害者的否决权。