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Strategy-Proof and Envy-Free Random Assignment

Christian Basteck and Lars Ehlers
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Christian Basteck: WZB Berlin
Lars Ehlers: Université de Montréal

No 307, Rationality and Competition Discussion Paper Series from CRC TRR 190 Rationality and Competition

Abstract: We study the random assignment of indivisible objects among a set of agents with strict preferences. We show that there exists no mechanism which is unanimous, strategy-proof and envy-free. Weakening the first requirement to q-unanimity – i.e., when every agent ranks a different object at the top, then each agent shall receive his most-preferred object with probability of at least q – we show that a mechanism satisfying strategy-proofness, envy-freeness and ex-post weak non-wastefulness can be q-unanimous only for q ≤ n2 (where n is the number of agents). To demonstrate that this bound is tight, we introduce a new mechanism, Random-Dictatorship-cum-Equal-Division (RDcED), and show that it achieves this maximal bound when all objects are acceptable. In addition, for three agents, RDcED is characterized by the first three properties and ex-post weak efficiency. If objects may be unacceptable, strategy-proofness and envy-freeness are jointly incompatible even with ex-post weak non-wastefulness.

Keywords: random assignment; strategy-proofness; envy-freeness; q-unanimity (search for similar items in EconPapers)
JEL-codes: D63 D70 (search for similar items in EconPapers)
Date: 2021-12-22
New Economics Papers: this item is included in nep-des and nep-mic
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