Strategy-Proof and Envy-Free Random Assignment

Basteck, Christian und Ehlers, Lars (22. Dezember 2021): Strategy-Proof and Envy-Free Random Assignment. Collaborative Research Center Transregio 190, Discussion Paper No. 307

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.

• Dokumententyp: Paper
• Keywords: random assignment; strategy-proofness; envy-freeness; q-unanimity
• Fakultät: Volkswirtschaft > Collaborative Research Center Transregio "Rationality and Competition"
• Themengebiete: 300 Sozialwissenschaften > 330 Wirtschaft
• JEL Classification: D63, D70
• Sprache: Englisch