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Related papers: Note on the size of a stable matching

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Stable matchings have been studied extensively in social choice literature. The focus has been mostly on integral matchings, in which the nodes on the two sides are wholly matched. A fractional matching, which is a convex combination of…

Computer Science and Game Theory · Computer Science 2022-04-20 Shivika Narang , Y Narahari

For most people, social contacts play an integral part in finding a new job. As observed by Granovetter's seminal study, the proportion of jobs obtained through social contacts is usually large compared to those obtained through postings or…

Computer Science and Game Theory · Computer Science 2009-10-07 Esteban Arcaute , Sergei Vassilvitskii

We study a one-to-one labor matching market. If a worker considers resigning from her current job to obtain a better one, how long does it take for this worker to actually get it? We present an algorithm that models this situation as a…

Theoretical Economics · Economics 2024-05-14 Agustin G. Bonifacio , Nadia Guiñazu , Noelia Juarez , Pablo Neme , Jorge Oviedo

We study the competition for partners in two-sided matching markets with heterogeneous agent preferences, with a focus on how the equilibrium outcomes depend on the connectivity in the market. We model random partially connected markets,…

Computer Science and Game Theory · Computer Science 2023-01-12 Yash Kanoria , Seungki Min , Pengyu Qian

In this paper we consider stable matchings subject to assignment constraints. These are matchings that require certain assigned pairs to be included, insist that some other assigned pairs are not, and, importantly, are stable. Our main…

Theoretical Economics · Economics 2024-06-14 Gregory Gutin , Philip R. Neary , Anders Yeo

We revisit the problem of designing optimal, individually rational matching mechanisms (in a general sense, allowing for cycles in directed graphs), where each player --- who is associated with a subset of vertices --- matches as many of…

Data Structures and Algorithms · Computer Science 2016-09-15 Avrim Blum , Ioannis Caragiannis , Nika Haghtalab , Ariel D. Procaccia , Eviatar B. Procaccia , Rohit Vaish

Assignment markets involve matching with transfers, as in labor markets and housing markets. We consider a two-sided assignment market with agent types and stochastic structure similar to models used in empirical studies, and characterize…

Computer Science and Game Theory · Computer Science 2014-07-10 Yash Kanoria , Daniela Saban , Jay Sethuraman

We propose a notion of concavity in two-sided many-to-one matching, which is an analogue to the balancedness condition in cooperative games. A stable matching exists when the market is concave. We provide a class of concave markets. In the…

Theoretical Economics · Economics 2023-09-11 Chao Huang

The stable matching problem sets the economic foundation of several practical applications ranging from school choice and medical residency to ridesharing and refugee placement. It is concerned with finding a matching between two disjoint…

Computer Science and Game Theory · Computer Science 2022-02-01 Angelina Brilliantova , Hadi Hosseini

We consider a many-to-one matching market where colleges share true preferences over students but make decisions using only independent noisy rankings. Each student has a true value $v$, but each college $c$ ranks the student according to…

Theoretical Economics · Economics 2024-02-27 Kenny Peng , Nikhil Garg

In the theory of two-sided matching markets there are two well-known models: the marriage model (where no money is involved) and the assignment model (where payments are involved). Roth and Sotomayor (1990) asked for an explanation for the…

Combinatorics · Mathematics 2007-05-23 Kimmo Eriksson , Johan Karlander

Two-sided popular matchings in bipartite graphs are a well-known generalization of stable matchings in the marriage setting, and they are especially relevant when preference lists are incomplete. In this case, the cardinality of a stable…

Discrete Mathematics · Computer Science 2018-03-13 Yuri Faenza , Vladlena Powers , Xingyu Zhang

We study the stable marriage problem in two-sided markets with randomly generated preferences. We consider agents on each side divided into a constant number of "soft tiers", which intuitively indicate the quality of the agent.…

Computer Science and Game Theory · Computer Science 2021-01-14 Itai Ashlagi , Mark Braverman , Amin Saberi , Clayton Thomas , Geng Zhao

We consider the problem of matching applicants to posts where applicants have preferences over posts. Thus the input to our problem is a bipartite graph G = (A U P,E), where A denotes a set of applicants, P is a set of posts, and there are…

Discrete Mathematics · Computer Science 2017-04-05 Prajakta Nimbhorkar , Arvind Rameshwar

Many important stable matching problems are known to be NP-hard, even when strong restrictions are placed on the input. In this paper we seek to identify structural properties of instances of stable matching problems which will allow us to…

Computer Science and Game Theory · Computer Science 2018-12-14 Kitty Meeks , Baharak Rastegari

Stable matching, a classical model for two-sided markets, has long been studied with little consideration for how each side's preferences are learned. With the advent of massive online markets powered by data-driven matching platforms, it…

Machine Learning · Computer Science 2020-07-14 Lydia T. Liu , Horia Mania , Michael I. Jordan

In this paper, we consider a many-to-one matching market where ties in the preferences of agents are allowed. For this market with capacity constraints, Bonifacio, Juarez, Neme, and Oviedo proved some relationship between the set of stable…

Computer Science and Game Theory · Computer Science 2024-05-02 Naoyuki Kamiyama

A firm-worker hypergraph consists of edges in which each edge joins a firm and its possible employees. We show that a stable matching exists in both many-to-one matching with transferable utilities and discrete many-to-one matching when the…

Theoretical Economics · Economics 2023-11-13 Chao Huang

Let $G = (A \cup B, E)$ be an instance of the stable marriage problem with strict preference lists. A matching $M$ is popular in $G$ if $M$ does not lose a head-to-head election against any matching where vertices are voters. Every stable…

Discrete Mathematics · Computer Science 2021-06-10 Agnes Cseh , Yuri Faenza , Telikepalli Kavitha , Vladlena Powers

We study a two-sided matching model where one side of the market (hospitals) has combinatorial preferences over the other side (doctors). Specifically, we consider the setting where hospitals have matroid rank valuations over the doctors,…

Computer Science and Game Theory · Computer Science 2025-02-28 Alon Eden , Vignesh Viswanathan , Yair Zick