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

TL;DR

This paper explores the design of fair and strategy-proof mechanisms for allocating identical objects among agents with money, revealing a tension between fairness and efficiency, and proposing a relaxation to achieve better outcomes.

Contribution

It characterizes mechanisms satisfying fairness, strategy-proofness, and no subsidy, and introduces a weaker incentive property to enable efficient, egalitarian-equivalent allocations.

Findings

Characterization of mechanisms with fairness and strategy-proofness constraints.

Relaxation to non-obvious manipulability enables efficient, fair allocations.

Identification of the agent optimal mechanism under the relaxed conditions.

Abstract

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.