Transparency in Allocation Problems

In centralized allocation problems participants have incomplete information about each others’ types. Hence, the designer may deviate from the announced allocation mechanism without the participants being able to detect these deviations. In this paper, I develop a theory of transparency in allocation problems; namely, I measure the transparency of a mechanism by the smallest number of participants that can detect any deviation. I find a striking result on the transparency of widespread allocation mechanisms: on one extreme, deviations from the Serial Dictatorship and the Immediate Acceptance mechanisms can always be detected by just two participants, while on the other extreme, deviations under the Deferred Acceptance and Top the Trading Cycles mechanisms may not be detected unless all information is publicly available. The finding potentially explains the widespread usage of Immediate Acceptance mechanism in practice despite its potentially inferior theoretical properties compared to Deferred Acceptance and Top Trading Cycles