Fair Matching under Constraints: Theory and Applications

Stability concepts in matching under distributional constraints

Many real matching markets are subject to distributional constraints. To guide market designers faced with constraints, we propose new stability concepts. A matching is strongly stable if satisfying blocking pairs inevitably violates a constraint. We show that a strongly stable matching may not exist, and that existence is guaranteed if and only if all distributional constraints are trivial. To...

MIMO Transmit Beampattern Matching Under Waveform Constraints

In this paper, the multiple-input multiple-output (MIMO) transmit beampattern matching problem is considered. The problem is formulated to approximate a desired transmit beampattern (i.e., an energy distribution in space and frequency) and to minimize the cross-correlation of signals reflected back to the array by considering different practical waveform constraints at the same time. Due to the...

Methods for history matching under geological constraints

Two geostatistical methods for history matching are presented. Both rely on the sequential simulation principle for generating geologically sound realizations. The first method relies on perturbing the sequential simulation through the perturbation of the conditional distribution models; the second method relies on the perturbation of random numbers. We show that both approaches are general in ...

Procedurally Fair and Stable Matching

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 andVandeVate, 1990, Ma, 1996). For both mechanisms we give various examples of probability distributions on the set of stable matchings and discuss properties that differentiate employment by lotto and th...

Applications of Matching Models under Preferences