The welfare effects of pre-arrangements in matching markets

We study the welfare effects of different types of pre-arrangements (as identified in Sönmez in J Econ Theory 86:148–156, 1999) under the intern-optimal and hospital-optimal stable mechanisms in matching markets. First, both mechanisms are manipulable via Type-2 pre-arrangements. Regarding the welfare consequences, they might cause inefficient outcomes to arise, and the welfare effects on each side are ambiguous in the sense that there might be agents from each side, apart from pre-arranging ones, being better and worse off. Then, for Type-1 pre-arrangements, due to Kojima and Pathak (Am Econ Rev 99(3):608–627, 2009), we know that the intern-optimal stable mechanism is immune to this type of manipulations. In contrast to this result, the hospital-optimal stable mechanism turns out to be manipulable. More interestingly, they do not result in inefficient outcomes, and the welfare effects on each side are unambiguous: All hospitals (interns) are better (worse) off.