We study many-to-one matchings, such as the assignment of students to colleges, where the students have preferences over the other students who would attend the same college. It is well known that the core of this model may be empty, without strong assumptions on agents' preferences. We...

Starting with an initial price vector, prices are adjusted in order to eliminate the demand excess and at the same time to keep the transfers to the sellers as low as possible. In each step of the auction, to which sellers should those transfers be made (minimal overdemanded sets) is the key...