Using the assignment of students to schools as our leading example, we study many-to-one two-sided matching markets without transfers. Students are endowed with cardinal preferences and schools with ordinal ones, while preferences of both sides need not be strict. Using the idea of a competitive...

This paper develops an integer programming approach to two-sided many-to-one matching by investigating stable integral matchings of a fictitious market where each worker is divisible. We show that stable matching exists in a discrete matching market when firms' preference profile satisfies a...

We study employment by lotto (Aldershof et al., 1999), a matching algorithm for the so-called stable marriage problem. We complement Aldershof et al.'s analysis in two ways. First, we give an alternative and intuitive description of employment by lotto. Second, we disprove Aldershof et al.'s...

We study procedurally fair matching mechanisms that produce stable matchings for the so-called marriage model of one-to-one, two-sided matching. Our main focus is on two such mechanisms: employment by lotto introduced by Aldershof et al. (1999) and the random order mechanism due to Roth and...

We motivate procedural fairness for matching mechanisms and study two procedurally fair and stable mechanisms: employment by lotto (Aldershof et al., 1999) and the random order mechanism (Roth and Vande Vate, 1990, Ma, 1996). For both mechanisms we give various examples of probability...

This paper revisits manipulation via capacities in centralized two-sided matching markets. Sönmez (1997) showed that no stable mechanism is nonmanipulable via capacities. We show that non-manipulability via capacities can be equivalently described by two types of non-manipulation via...