We consider manipulations in the context of coalitional games, where a coalition aims to increase the total payoff of its members. An allocation rule is immune to coalitional manipulation if no coalition can benefit from internal reallocation of worth on the level of its subcoalitions (reallocation-proofness), and if no coalition benefits from a lower worth while all else remains the same (weak coalitional monotonicity). Replacing additivity in Shapley's original characterization by these requirements yields a new foundation of the Shapley value, i.e., it is the unique efficient and symmetric allocation rule that awards nothing to a null player and is immune to coalitional manipulations. We further find that for efficient allocation rules, reallocation-proofness is equivalent to constrained marginality, a weaker variant of Young's marginality axiom. Our second characterization improves upon Young's characterization by weakening the independence requirement intrinsic to marginality.

翻译：本文考虑联盟博弈中的操纵问题，其中联盟旨在增加其成员的总收益。若分配规则满足以下条件，则称其对联盟操纵具有免疫性：任何联盟无法通过其子联盟内部的价值再分配获益（再分配无懈可击性），且当其他条件不变时，任何联盟无法通过降低自身价值获益（弱联盟单调性）。将沙普利原始公理化体系中的可加性替换为上述条件，可得到沙普利值的新基础——即它是唯一满足以下性质的对称分配规则：对无效玩家分配零值、具有效率性且对联盟操纵具有免疫性。进一步发现，对于效率性分配规则，再分配无懈可击性等价于约束边际性，这是杨格边际性公理的一种弱化形式。我们的第二个刻画通过削弱边际性公理所内蕴的独立性要求，改进了杨格的经典公理化结果。