Abstract
We present a possibility result on the existence of a random assignment rule satisfying sd-strategy-proofness, sd-efficiency, and equal treatment of equals. In particular, we introduce a class of preference domains: sequentially dichotomous domains. On any such domain, the probabilistic serial rule (Bogomolnaia and Moulin (2001)) is sd-strategy-proof. Moreover, any sequentially dichotomous domain is maximal for this rule to be sd-strategy-proof.
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