English
Related papers

Related papers: Stable matching in a common generalization of the …

200 papers

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

In 1962, Gale and Shapley \cite{GS} introduced the concept of stable marriages and proved their existence. Since then, the statement of the stability problem has been highly generalized. And a lot of proofs has emerged for the existence in…

Theoretical Economics · Economics 2025-05-20 V. I. Danilov

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

We propose a generalization of the classical stable marriage problem. In our model, the preferences on one side of the partition are given in terms of arbitrary binary relations, which need not be transitive nor acyclic. This generalization…

Computer Science and Game Theory · Computer Science 2014-07-28 Linda Farczadi , Konstantinos Georgiou , Jochen Könemann

We study many-to-one matching problems between institutions and individuals, where each institution may be matched to multiple individuals. The matching market includes couples, who view pairs of institutions as complementary. Institutions'…

Theoretical Economics · Economics 2025-07-11 Shashwat Khare , Souvik Roy

We focus on the one-to-one two-sided matching model with two disjoint sets of agents of equal size, where each agent in a set has preferences on the agents in the other set modeled by a linear order. A matching mechanism associates a set of…

Theoretical Economics · Economics 2024-11-27 Daniela Bubboloni , Michele Gori , Claudia Meo

I introduce a stability notion, dynamic stability, for two-sided dynamic matching markets where (i) matching opportunities arrive over time, (ii) matching is one-to-one, and (iii) matching is irreversible. The definition addresses two…

Theoretical Economics · Economics 2021-03-01 Laura Doval

In many economic contexts, agents from a same population team up to better exploit their human capital. In such contexts (often called "roommate matching problems"), stable matchings may fail to exist even when utility is transferable. We…

General Economics · Economics 2021-02-15 Pierre-André Chiappori , Alfred Galichon , Bernard Salanié

Several countries successfully use centralized matching schemes for school or higher education assignment, or for entry-level labour markets. In this paper we explore the computational aspects of a possible similar scheme for assigning…

Data Structures and Algorithms · Computer Science 2015-01-26 Katarina Cechlarova , Tamas Fleiner , David F. Manlove , Iain McBride

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

In this paper we consider the issue of a unique prediction in one to one two sided matching markets, as defined by Gale and Shapley (1962), and we prove the following. Theorem. Let P be a one-to-one two-sided matching market and let P be…

Theoretical Economics · Economics 2023-07-21 Gregory Z. Gutin , Philip R. Neary , Anders Yeo

We study the variant of the stable marriage problem in which the preferences of the agents are allowed to include indifferences. We present a mechanism for producing Pareto-stable matchings in stable marriage markets with indifferences that…

Computer Science and Game Theory · Computer Science 2017-10-13 Nevzat Onur Domaniç , Chi-Kit Lam , C. Gregory Plaxton

Matching games is a one-to-one two sided market model introduced by Garrido-Lucero and Laraki, in which coupled agents' utilities are endogenously determined as the outcome of a strategic game. They refine the classical pairwise stability…

Computer Science and Game Theory · Computer Science 2025-07-22 Felipe Garrido-Lucero , Rida Laraki

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

In the Stable Marriage Problem two sets of agents must be paired according to mutual preferences, which may happen to conflict. We present two generalizations of its sex-oriented version, aiming to take into account correlations between the…

Disordered Systems and Neural Networks · Physics 2009-11-07 G. Caldarelli , Andrea Capocci , Paolo Laureti

We propose and investigate a model for mate searching and marriage in large societies based on a stochastic matching process and simple decision rules. Agents have preferences among themselves given by some probability distribution. They…

Theoretical Economics · Economics 2021-08-20 Davi B. Costa

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 a many-to-many matching model in which agents' preferences satisfy substitutability and the law of aggregate demand, we present an algorithm to compute the full set of stable matchings. This algorithm relies on the idea of "cycles in…

Theoretical Economics · Economics 2024-04-25 Agustin G. Bonifacio , Noelia Juarez , Pablo Neme , Jorge Oviedo

We present a fascinating model that has lately caught attention among physicists working in complexity related fields. Though it originated from mathematics and later from economics, the model is very enlightening in many aspects that we…

Physics and Society · Physics 2021-03-23 Enrico Maria Fenoaltea , Izat B. Baybusinov , Jianyang Zhao , Lei Zhou , Yi-Cheng Zhang

Let $L$ be any finite distributive lattice and $B$ be any boolean predicate defined on $L$ such that the set of elements satisfying $B$ is a sublattice of $L$. Consider any subset $M$ of $L$ of size $k$ of elements of $L$ that satisfy $B$.…

Discrete Mathematics · Computer Science 2020-01-10 Vijay K. Garg