Strategy-proofness and identical preferences lower bound in allocation problem of indivisible objects

We study an allocation problem of heterogeneous indivisible objects among agents without money. Each agent receives at most one object and prefers any object to nothing. We identify the class of rules satisfying strategy-proofness, Pareto-efficiency, and the identical preferences lower bound. Each rule of this class is included in Papai's (Econometrica 68:1403-1433, 2000) rules and can be described by a top trading cycle rule associated with an inheritance structure that satisfies a symmetry condition called U-symmetry.