We study the problem of allocating heterogeneous indivisible objects (e.g. jobs, houses, etc.) when monetary compensations are possible. We present a new family of strategy-proof and envy-free mechanisms. Each mechanism in the family is a variation of the Vickrey-Clarke-Groves pivotal mechanism: the planner selects tentative compensations associated with the indivisible objects and implements the pivotal mechanism for the objects with tentative compensations. We characterize this family as the "Pareto dominant" class of strategy-proof and envy-free mechanisms in the two-agent case.
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