Assignment Rules of a Single Indivisible Object Under the Full Preference Domain

Abstract

We consider the allocation problem of a single indivisible object to one of several agents under the full preference domain when monetary transfers are not allowed. Our central requirement is strategy-proofness. The additional properties we seek are Pareto optimality, non-dictatorship, and non-bossiness. We provide characterizations of strategy-proof rules that satisfy two out of three additional properties: Pareto optimality and non-bossiness; non-dictatorship and non-bossiness; and Pareto optimality and non-dictatorship. As a consequence of these characterizations, we show that a strategy-proof rule cannot satisfy these three additional properties simultaneously.