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.

在协作联盟游戏中，我们研究了协作联盟为了增加成员的总收益而进行的操纵行为。我们提出了一种新的 Shapley 值的基础，该值是唯一的高效和对联盟操纵免疫的分配规则，它将空置玩家分配为零，并满足弱协作单调性和次协作联盟再分配免疫性。此外，我们还发现对于高效的分配规则，次协作联盟再分配免疫性等价于约束边际性，这是 Young 的边际性公理的一种较弱变体。我们的第二个特征改进了 Young 的特征，从而减弱了边际性内在的独立性要求。

合作联盟的操纵和 Shapley 价值的免疫性

Coalitional Manipulations and Immunity of the Shapley Value

Rationing of healthcare resources has emerged as an important issue, which
has been discussed by medical experts, policy-makers, and the general public.
We consider a rationing problem where medical units are to be allocated to
patients. Each unit is reserved for one of several categories and each category
has a priority ranking of the patients. We present an allocation rule that
respects the priorities, complies with the eligibility requirements, allocates
the largest feasible number of units, and does not incentivize agents to hide
that they qualify through a category. The rule characterizes all possible
allocations that satisfy the first three properties and is polynomial-time
computable.

该研究论文探讨了医疗资源的配给问题，提出了一种满足优先级、资格要求和尽可能分配最多资源的分配规则，同时保持了计算效率。