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We study stable matching problems with locality of information and control. In our model, each agent is a node in a fixed network and strives to be matched to another agent. An agent has a complete preference list over all other agents it…

Data Structures and Algorithms · Computer Science 2016-11-22 Martin Hoefer , Lisa Wagner

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…

Computer Science and Game Theory · Computer Science 2020-05-19 Simon Mauras

We present a generalization of the marriage problem underlying Hall's famous Marriage Theorem to what we call the Symmetric Marriage Problem, a problem that can be thought of as a special case of Maximal Weighted Bipartite Matching. We show…

Combinatorics · Mathematics 2020-01-22 Jonathan Lenchner

In the marriage problem, a variant of the bi-parted matching problem, each member has a `wish-list' expressing his/her preference for all possible partners; this list consists of random, positive real numbers drawn from a certain…

Disordered Systems and Neural Networks · Physics 2015-06-25 Th. M. Nieuwenhuizen

We provide a problem definition of the stable marriage problem for a general number of parties $p$ under a natural preference scheme in which each person has simple lists for the other parties. We extend the notion of stability in a natural…

Computer Science and Game Theory · Computer Science 2015-09-11 Jared D. Lichtman

The use of combinatorial optimization algorithms has contributed substantially to the major progress that has occurred in recent years in the understanding of the physics of disordered systems, such as the random-field Ising model. While…

Disordered Systems and Neural Networks · Physics 2023-02-22 Manoj Kumar , Martin Weigel

Consider the group of $n$ men and $n$ women, each with their own preference list for a potential marriage partner. The stable marriage is a bipartite matching such that no unmatched pair (man, woman) prefer each other to their partners in…

Combinatorics · Mathematics 2017-07-25 Boris Pittel

For a two-sided ($n$ men/$n$ women) stable matching problem) Gale and Shapley studied a proposal algorithm (men propose/women select, or the other way around), that determines a matching, not blocked by any unmatched pair. Irving used this…

Combinatorics · Mathematics 2020-05-15 Boris Pittel

In two-sided matching markets, the agents are partitioned into two sets. Each agent wishes to be matched to an agent in the other set and has a strict preference over these potential matches. A matching is stable if there are no blocking…

Computer Science and Game Theory · Computer Science 2013-02-26 Georgios Askalidis , Nicole Immorlica , Emmanouil Pountourakis

In a stable matching problem there are two groups of agents, with agents on one side having their individual preferences for agents on another side as a potential match. It is assumed silently that agents can freely and costlessly ``switch"…

Combinatorics · Mathematics 2025-07-22 Boris Pittel , Kirill Rudov

We consider the two-sided stable matching setting in which there may be uncertainty about the agents' preferences due to limited information or communication. We consider three models of uncertainty: (1) lottery model --- in which for each…

Computer Science and Game Theory · Computer Science 2016-07-12 Haris Aziz , Péter Biró , Serge Gaspers , Ronald de Haan , Nicholas Mattei , Baharak Rastegari

The stable matching problem has been the subject of intense theoretical and empirical study since the seminal 1962 paper by Gale and Shapley. The number of stable matchings for different systems of preferences has been studied in many…

Probability · Mathematics 2024-01-01 Christopher Hoffman , Avi Levy , Elchanan Mossel

In the stable marriage problem, a set of men and a set of women are given, each of whom has a strictly ordered preference list over the acceptable agents in the opposite class. A matching is called stable if it is not blocked by any pair of…

Discrete Mathematics · Computer Science 2019-07-25 Ágnes Cseh , Klaus Heeger

We study stable matchings that are robust to preference changes in the two-sided stable matching setting of Gale and Shapley [GS62]. Given two instances $A$ and $B$ on the same set of agents, a matching is said to be robust if it is stable…

Computer Science and Game Theory · Computer Science 2026-01-14 Rohith Reddy Gangam , Tung Mai , Nitya Raju , Vijay V. Vazirani

In this article we study the stable marriage game induced by the men-proposing Gale-Shapley algorithm. Our setting is standard: all the lists are complete and the matching mechanism is the men-proposing Gale-Shapley algorithm. It is well…

Data Structures and Algorithms · Computer Science 2015-09-16 Sushmita Gupta , Kazuo Iwama , Shuichi Miyazaki

Gale and Shapley introduced a matching problem between two sets of agents where each agent on one side has an exogenous preference ordering over the agents on the other side. They defined a matching as stable if no unmatched pair can both…

Computer Science and Game Theory · Computer Science 2025-02-27 Felipe Garrido-Lucero , Rida Laraki

We study the classical, two-sided stable marriage problem under pairwise preferences. In the most general setting, agents are allowed to express their preferences as comparisons of any two of their edges and they also have the right to…

Discrete Mathematics · Computer Science 2018-10-02 Ágnes Cseh , Attila Juhos

In the Gale-Shapley model of two-sided matching, it is well known that for generic preferences, the outcomes for each side can vary dramatically in the male-optimal vs. female-optimal stable matchings. In this paper, we show that under a…

Theoretical Economics · Economics 2026-03-26 Bill Wang

We study deviations by a group of agents in the three main types of matching markets: the house allocation, the marriage, and the roommates models. For a given instance, we call a matching $k$-stable if no other matching exists that is more…

Discrete Mathematics · Computer Science 2023-07-11 Haris Aziz , Gergely Csáji , Ágnes Cseh

Stable marriage of a two-sided market with unit demand is a classic problem that arises in many real-world scenarios. In addition, a unique stable marriage in this market simplifies a host of downstream desiderata. In this paper, we explore…

Computer Science and Game Theory · Computer Science 2024-08-05 Kartik Gokhale , Amit Kumar Mallik , Ankit Kumar Misra , Swaprava Nath