Coalitional Manipulations and Immunity of the Shapley Value
Christian Basteck Frank Huettner
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.