The manipulability of fair solutions in assignment of an indivisible object with monetary transfers

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.