Maximal Manipulation in Fair Allocation

We consider the problems of fairly allocating indivisible objects and money. The objective of the present study is to examine strategic manipulation under envy-free solutions. We show that each individual obtains the welfare level of his "optimal" envy-free allocation by maximally manipulating the solutions. This maximal manipulation theorem leads to several meaningful results concerning the manipulability of envy-free solutions: (i) we present a characterization of "non-manipulable" preference profiles under a given envy-free solution; (ii) we analyze the set of Nash equilibrium allocations in the direct revelation games associated with a given envy-free solution; (iii) we formulate envy-free solutions that are strategy-proof for at least one individual; and (iv) we identify the functional form of the least manipulable envy-free solutions on the quasi-linear domain.

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