Public decision making often involves the problem of fairly assigning one indivisible object to agents with monetary transfers. An example is the choice of the location of a garbage incineration facility where the accepting district should receive fair compensations from other districts. In this problem, we show that for broad classes of solutions satisfying a welfare lower bound and an efficiency-oriented condition, the set of equilibrium allocations in the manipulation game associated with a given solution coincides with the set of all envy-free allocations. This generalizes Tadenuma and Thomson's equivalence result for a class of envy-free solutions. Our result covers the Shapley value, which is not covered by Tadenuma and Thomson's result.
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