Fair and group strategy-proof good allocation with money

We completely characterize the class of fair and group strategy-proof mechanisms. We consider two notions of fairness, anonymity in welfare and no-envy. Both fairness axioms, when applied with strategy-proofness, imply decision efficiency, and lead to the same class of group strategy-proof mechanisms (where the group size is restricted to two). We find that the only feasible mechanism satisfying a mild zero transfer axiom, in this class, is the Pivotal mechanism.

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