Related papers: Stable Matching: Dealing with Changes in Preferenc…
We study variants of the stable marriage and college admissions models in which the agents are allowed to express weak preferences over the set of agents on the other side of the market and the option of remaining unmatched. For the…
We introduce a generalized version of the famous Stable Marriage problem, now based on multi-modal preference lists. The central twist herein is to allow each agent to rank its potentially matching counterparts based on more than one…
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…
In bipartite matching problems, agents on two sides of a graph want to be paired according to their preferences. The stability of a matching depends on these preferences, which in uncertain environments also reflect agents' beliefs about…
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…
The Stable Roommates problem involves matching a set of agents into pairs based on the agents' strict ordinal preference lists. The matching must be stable, meaning that no two agents strictly prefer each other to their assigned partners. A…
This paper examines equilibria in dynamic two-sided matching games, extending Gale and Shapley's foundational model to a non-cooperative, decentralized, and dynamic framework. We focus on markets where agents have utility functions and…
In stable matching, one must find a matching between two sets of agents, commonly men and women, or job applicants and job positions. Each agent has a preference ordering over who they want to be matched with. Moreover a matching is said to…
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…
Recently MV18 identified and initiated work on the new problem of understanding structural relationships between the lattices of solutions of two "nearby" instances of stable matching. They also gave an application of their work to finding…
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…
In the stable marriage and roommates problems, a set of agents is given, each of them having a strictly ordered preference list over some or all of the other agents. A matching is a set of disjoint pairs of mutually accepted agents. If any…
We study the three-dimensional stable matching problem with cyclic preferences. This model involves three types of agents, with an equal number of agents of each type. The types form a cyclic order such that each agent has a complete…
We consider the three-dimensional stable matching problem with cyclic preferences, a problem originally proposed by Knuth. Despite extensive study of the problem by experts from different areas, the question of whether every instance of…
In the fundamental Stable Marriage and Stable Roommates problems, there are inherent trade-offs between the size and stability of solutions. While in the former problem, a stable matching always exists and can be found efficiently using the…
The classical Stable Roommates problem is to decide whether there exists a matching of an even number of agents such that no two agents which are not matched to each other would prefer to be with each other rather than with their…
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…
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…
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?…
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…