Mechanism design is addressed in the context of fair allocations of indivisible goods with monetary compensation. Motivated by a real-world social choice problem, mechanisms with verification are considered in a setting where (i) agents declarations on allocated goods can be fully verified before payments are performed, and where (ii) verification is not used to punish agents whose declarations resulted in incorrect ones. Within this setting, a mechanism is designed that is shown to be truthful, efficient, and budget-balanced, and where agents utilities are fairly determined by the Shapley value of suitable coalitional games. The proposed mechanism is however shown to be #P-complete. Thus, to deal with applications with many agents involved, two polynomial-time randomized variants are also proposed: one that is still truthful and efficient, and which is approximately budget-balanced with high probability, and another one that is truthful in expectation, while still budget-balanced and efficient.
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