Coalitional Manipulations and Immunity of the Shapley Value
This work addresses theoretical robustness in cooperative game theory, offering incremental refinements to existing characterizations of the Shapley value.
The paper tackles the problem of coalitional manipulations in cooperative games by introducing immunity conditions, and it shows that the Shapley value is uniquely characterized by these conditions, providing a new axiomatic foundation.
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.