Egalitarian-equivalent and strategy-proof mechanisms in homogeneous multi-object allocation problems

We study the problem of allocating homogeneous and indivisible objects among agents with money. In particular, we investigate the relationship between egalitarian-equivalence (Pazner and Schmeidler, 1978), as a fairness concept, and efficiency under agents' incentive constraints. As a first result, we characterize the class of mechanisms that satisfy egalitarian-equivalence, strategy-proofness, individual rationality, and no subsidy. Our characterization reveals a strong tension between egalitarian-equivalence and efficiency: under these properties, the mechanisms allocate objects only in limited cases. To address this limitation, we replace strategy-proofness with the weaker incentive property, non-obvious manipulability (Troyan and Morrill, 2020). We show that this relaxation allows us to design mechanisms that achieve efficiency while still ensuring egalitarian-equivalence. Furthermore, upon achieving efficiency, we identify the agent optimal mechanism in the characterized class.