Stability and Median Rationalizability for Aggregate Matchings

Aggregate Matchings ∗ Federico Echenique

This paper characterizes the testable implications of stability for aggregate matchings. We consider data on matchings where individuals are aggregated, based on their observable characteristics, into types, and we know how many agents of each type match. We derive stability conditions for an aggregate matching, and, based on these, provide a simple necessary and sufficient condition for an obs...

Stable Roommates Matchings, Mirror Posets, Median Graphs, and the Local/Global Median Phenomenon in Stable Matchings

For stable marriage (SM) and solvable stable roommates (SR) instances, it is known that there are stable matchings that assign each participant to his or her (lower/upper) median stable partner. Moreover, for SM instances, a stable matching has this property if and only if it is a median of the distributive lattice formed by the instance’s stable matchings. In this paper, we show that the above...

Evaluation of fractal dimensions for analysis of aggregate stability

Median stable matchings in two-sided markets

We show that generalized median stable matchings exist in many-to-many matching markets when contracts are strong substitutes and satisfy the law of aggregate demand.

Stability vs. Cost of Matchings

This paper studies the classic minimum-cost perfect matching problem in complete graphs under certain stability constraints. Given some real α ≥ 1, a matching M is said to be α-stable if there does not exist any edge (x, y) / ∈ M such that α · w(x, y) < min{w(x, x′), w(y, y′)}, where x′ and y′ are the vertices matched to x and y, respectively, under M . Given some real β ≥ 1, the perfect matchi...