Random assignments on preference domains with a tier structure - LIU, Peng (Institutional Knowledge at Singapore Management University, 2017)
We address a standard random assignment problem (Bogomolnaia and Moulin (2001)) and search forsd-strategy-proof, sd-efficient and sd-envy-free or equal-treatment-of-equals rules.Our main result is that on a connected domain (Sato (2013)),if there exists a rule satisfying these axioms, this domain is endowed with a restricted tier structure.Furthermore, we show that, on such a domain, the Probabilistic Serial rule is the unique rulethat satisfies these axioms.As an extension, we introduce outside options to the model, and establish the same characterizations.