タイトル：Strategy-proofness, Efficiency, and the Core in Matching Problems with Transfers
【abstract】 We study a class of one-to-one matching problems in which monetary transfers are possible. Sönmez (1999, Econometrica 67: 677–689) establishes
that, for a general class of indivisible goods allocation problems without monetary transfers, if an allocation rule satisfies strategy-proofness,
efficiency, and individual rationality, then, for each preference profile under which the core is non-empty, each pair of core allocations are
Pareto-indifferent and the allocation chosen by the rule is in the core. In this study, we show that the result of Sönmez (1999) extends to our
environment if an allocation rule satisfies no subsidy in addition to the three properties. As a corollary of this result, we show that, under
individual rationality and no subsidy, efficiency is incompatible with strategy-proofness in many situations. We also establish that, in the two-sided matching problem with transfers,
the “one-sided optimal core allocation rule” is the only rule that satisfies one-sided strategy-proofness, efficiency, individual rationality, and no subsidy.