Related papers: Two-sided matching with firms' complementary prefe…
I relate bipartite graph matchings to stable matchings. I prove a necessary and sufficient condition for the existence of a saturating stable matching, where every agent on one side is matched, for all possible preferences. I extend my…
Following up on purely theoretical work of Bredereck et al. [AAAI 2020], we contribute further theoretical insights into adapting stable two-sided matchings to change. Moreover, we perform extensive empirical studies hinting at numerous…
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…
Stable matching in a community consisting of men and 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, who…
In discrete matching markets, substitutes and complements can be unidirectional between two groups of workers when members of one group are more important or competent than those of the other group for firms. We show that a stable matching…
We consider a many-to-one variant of the stable matching problem. More concretely, we consider the variant of the stable matching problem where one side has a matroid constraint. Furthermore, we consider the situation where the preference…
In several two-sided markets, including labor and dating, agents typically have limited information about their preferences prior to mutual interactions. This issue can result in matching frictions, as arising in the labor market for…
In two-sided matching markets, ensuring both stability and strategy-proofness poses a significant challenge; it is impossible when agents' preferences are unrestricted. But what if agents' preferences have specific restricted structures?…
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…
Many two-sided matching markets, from labor markets to school choice programs, use a clearinghouse based on the applicant-proposing deferred acceptance algorithm, which is well known to be strategy-proof for the applicants. Nonetheless, a…
Consider a cyclically ordered collection of $r$ equinumerous agent sets with strict preferences of every agent over the agents from the next agent set. A weakly stable cyclic matching is a partition of the set of agents into disjoint union…
We study the existence of stable matchings when agents have choice correspondences instead of preference relations. We extend the framework of \cite{chambers2017choice} by weakening the path independence assumption. For many-to-many…
Many-to-one matching markets exist in numerous different forms, such as college admissions, matching medical interns to hospitals for residencies, assigning housing to college students, and the classic firms and workers market. In all these…
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…
We propose two solution concepts for matchings under preferences: robustness and near stability. The former strengthens while the latter relaxes the classic definition of stability by Gale and Shapley (1962). Informally speaking, robustness…
We consider a learning problem for the stable marriage model under unknown preferences for the left side of the market. We focus on the centralized case, where at each time step, an online platform matches the agents, and obtains a noisy…
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…
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…
We study conditions for the existence of stable and group-strategy-proof mechanisms in a many-to-one matching model with contracts if students' preferences are monotone in contract terms. We show that "equivalence", properly defined, to a…
We study uncoordinated matching markets with additional local constraints that capture, e.g., restricted information, visibility, or externalities in markets. Each agent is a node in a fixed matching network and strives to be matched to…