On obviously strategy-proof implementation of fixed priority top trading cycles with outside options

We study the implementation of a fixed priority top trading cycles (FPTTC) rule via an obviously strategy-proof (OSP) mechanism (Li, 2017) in the context of assignment problems with outside options, where agents are to be assigned at most one indivisible object and monetary transfers are not allowed. In a model without outside options, Troyan (2019) gives a sufficient (but not necessary) and Mandal and Roy (2020) give a necessary and sufficient condition for an FPTTC rule to be OSP-implementable. This paper shows that in a model with outside options, the two conditions (in Troyan (2019) and Mandal and Roy (2020)) are equivalent for an FPTTC rule, and each of them is necessary and sufficient for an FPTTC rule to be OSP-implementable. (C) 2021 Elsevier B.V. All rights reserved.