On popularity-based random matching markets

04/08/2019
by   Hugo Gimbert, et al.
0

Stable matching in a community consisting of N men and N women is a classical combinatorial problem that has been the subject of intense theoretical and empirical study since its introduction in 1962 in a seminal paper by Gale and Shapley [GS62]. In this paper, we study the number of stable pairs, that is, the man/woman pairs that appear in some stable matching. We prove that if the preference lists on one side are generated at random using the popularity model of Immorlica and Mahdian [IM15], the expected number of stable edges is bounded by N + N ln N , matching the asymptotic bound for uniform preference lists. If in addition that popularity model is a geometric distribution, then the number of stable edges is O(N) and the incentive to manipulate is limited. If in addition the preference lists on the other side are uniform, then the number of stable edges is asymptotically N up to lower order terms: most participants have a unique stable partner, hence non-manipulability.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/18/2020

Two-Sided Random Matching Markets: Ex-Ante Equivalence of the Deferred Acceptance Procedures

Stable matching in a community consisting of N men and N women is a clas...
research
05/17/2020

On the (Parameterized) Complexity of Almost Stable Marriage

In the Stable Marriage problem. when the preference lists are complete, ...
research
04/16/2018

Preference Cycles in Stable Matchings

Consider the stable matching problem on two sets. We introduce the conce...
research
04/09/2019

Stability-Preserving, Incentive-Compatible, Time-Efficient Mechanisms for Increasing School Capacity

We address the following dynamic version of the school choice question: ...
research
05/07/2021

Maximally Satisfying Lower Quotas in the Hospitals/Residents Problem with Ties

Motivated by a serious issue that hospitals in rural areas suffer from s...
research
04/08/2022

Stable Matching: Choosing Which Proposals to Make

Why does stable matching work well in practice despite agents only provi...
research
03/13/2022

Incomplete List Setting of the Hospitals/Residents Problem with Maximally Satisfying Lower Quotas

To mitigate the imbalance in the number of assignees in the Hospitals/Re...

Please sign up or login with your details

Forgot password? Click here to reset