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Matching algorithms have demonstrated great success in several practical applications, but they often require centralized coordination and plentiful information. In many modern online marketplaces, agents must independently seek out and…

Computer Science and Game Theory · Computer Science 2025-01-14 Vade Shah , Bryce L. Ferguson , Jason R. Marden

We study a dynamic model of the relationship between two people where the states depend on the "power" in the relationship. We perform a comprehensive analysis of stability of the system, and determine a set of conditions under which stable…

Multiagent Systems · Computer Science 2023-09-15 Sam Ganzfried

In many-to-many matching models, substitutable preferences constitute the largest domain for which a pairwise stable matching is guaranteed to exist. In this note, we extend the recently proposed algorithm of Hatfield et al. [3] to test…

Computer Science and Game Theory · Computer Science 2012-01-04 Haris Aziz , Markus Brill , Paul Harrenstein

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

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

The Hospitals / Residents problem with Couples (HRC) models the allocation of intending junior doctors to hospitals where couples are allowed to submit joint preference lists over pairs of (typically geographically close) hospitals. It is…

Data Structures and Algorithms · Computer Science 2016-06-21 David F. Manlove , Iain McBride , James Trimble

We study the problem of finding solutions to the stable matching problem that are robust to errors in the input and we obtain a polynomial time algorithm for a special class of errors. In the process, we also initiate work on a new…

Data Structures and Algorithms · Computer Science 2018-12-17 Tung Mai , Vijay V. Vazirani

This paper has two objectives. One is to give a linear time algorithm that solves the stable roommates problem (i.e., obtains one stable matching) using the stable marriage problem. The idea is that a stable matching of a roommate instance…

Computational Complexity · Computer Science 2023-05-23 Kazuo Iwama , Shuichi Miyazaki

This paper describes the transition of a male-pessimal matching set to optimal when it is a man-oriented approach by deleting a pair from matching set considering the score based approach. A descriptive explanation of the proposed algorithm…

Data Structures and Algorithms · Computer Science 2014-01-20 Ekta Gupta , Kalyani , Nitin

In a many-to-one matching model in which firms' preferences satisfy substitutability, we study the set of worker-quasi-stable matchings. Worker-quasi-stability is a relaxation of stability that allows blocking pairs involving a firm and an…

Theoretical Economics · Economics 2022-03-04 Agustin G. Bonifacio , Nadia Guinazu , Noelia Juarez , Pablo Neme , Jorge Oviedo

Finding a stable matching is one of the central problems in algorithmic game theory. If participants are allowed to have ties and incomplete preferences, computing a stable matching of maximum cardinality is known to be NP-hard. In this…

Computer Science and Game Theory · Computer Science 2020-07-15 Jochen Koenemann , Kanstantsin Pashkovich , Natig Tofigzade

We study a practical centralized matching problem which assigns children to daycare centers. The collective preferences of siblings from the same family introduce complementarities, which can lead to the absence of stable matchings, as…

Computer Science and Game Theory · Computer Science 2025-01-23 Zhaohong Sun , Tomohiko Yokoyama , Makoto Yokoo

The stable roommates problem does not necessarily have a solution, i.e. a stable matching. We had found that, for the uniformly random instance, the expected number of solutions converges to $e^{1/2}$ as $n$, the number of members, grows,…

Combinatorics · Mathematics 2017-05-24 Boris Pittel

In the multidimensional stable roommate problem, agents have to be allocated to rooms and have preferences over sets of potential roommates. We study the complexity of finding good allocations of agents to rooms under the assumption that…

Computer Science and Game Theory · Computer Science 2020-05-01 Niclas Boehmer , Edith Elkind

Pairwise comparison matrices often exhibit inconsistency, therefore many indices have been suggested to measure their deviation from a consistent matrix. A set of axioms has been proposed recently that is required to be satisfied by any…

Artificial Intelligence · Computer Science 2020-05-28 László Csató

We study the many-to-many bipartite matching problem in the presence of preferences where ties, as well as lower quotas, may appear on both sides of the bipartition. The input is a bipartite graph $G=(A \cup B, E)$, where each vertex in $A…

Data Structures and Algorithms · Computer Science 2026-03-10 Meghana Nasre , Prajakta Nimbhorkar , Keshav Ranjan

We study the Popular Matching problem in multiple models, where the preferences of the agents in the instance may change or may be unknown/uncertain. In particular, we study an Uncertainty model, where each agent has a possible set of…

Computer Science and Game Theory · Computer Science 2025-06-06 Gergely Csáji

We study the implementability of stable matchings in a two-sided market model with one-sided incomplete information. Firms' types are publicly known, whereas workers' types are private information. A mechanism generates a matching and…

Theoretical Economics · Economics 2025-12-23 Dinko Dimitrov , Dipjyoti Majumdar

The Stable Marriage Problem (SMP) has been extremely discussed in the literature and it is useful to a number of real-world applications. We propose a generalized version of the SMP in which numbers of the matching groups are different as…

Social and Information Networks · Computer Science 2019-02-26 Bernardo Alves Furtado

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