Pairwise kidney exchange: Comment

In their recent paper, Roth et al. [Pairwise kidney exchange, J. Econ. Theory 125 (2005) 151-188] consider pairwise kidney exchanges, and show within this subset of feasible exchanges that a priority mechanism is strategy-proof. We show that this result can be broadened to allow much more general mechanisms and restrictions on the feasible set of allocations, including allowing three-way exchanges, regional specifications, and others. The key requirement is that the choice mechanism be consistent, i.e., if an allocation is chosen from some set of feasible allocations, it is also chosen from any subset of that set.