Object reallocation problems with single-dipped preferences

For object reallocation problems, TTC is the leading rule: if preferences are strict but otherwise unrestricted, it is the only rule satisfying efficiency, the endowments lower bounds, and strategy-proofness (Ma, 1994); moreover, it is the only rule satisfying the endowments lower bounds, strategy-proofness, and endowment-swapping-proofness (Fujinaka and Wakayama, 2018). We focus on the domain of single-dipped preferences, and ask whether these results hold there. We show that they do. Returning to preferences that are strict but otherwise unrestricted, TTC is not “obviously strategy-proof” (Li, 2017). Again we ask if this remains true on the domain of single-dipped preferences, and show that on this domain, TTC does satisfy this property. Moreover, the domain of single-dipped preferences is a maximal domain on which TTC is obviously strategy-proof.