Maximal Manipulation in Fair Allocation

We herein 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 therefore investigate the consequence of individual manipulation. Each individual is observed to obtain the welfare level of his “optimal” envy-free allocation by maximally manipulating the solutions. This maximal manipulation theorem leads to several fruitful results on 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.