Related papers: Stable marriage and roommate problems with individ…
The formal study of coalition formation in multi-agent systems is typically realized in the framework of hedonic games, which originate from economic theory. The main focus of this branch of research has been on the existence and the…
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…
The stable marriage problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools, or more generally to any two-sided market. We consider a useful variation of the…
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…
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…
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…
When computing stable matchings, it is usually assumed that the preferences of the agents in the matching market are fixed. However, in many realistic scenarios, preferences change over time. Consequently, an initially stable matching may…
Hedonic games provide a natural model of coalition formation among self-interested agents. The associated problem of finding stable outcomes in such games has been extensively studied. In this paper, we identify simple conditions on…
The Stable Roommates problems are characterized by the preferences of agents over other agents as roommates. A solution is a partition of the agents into pairs that are acceptable to each other (i.e., they are in the preference lists of…
The stable marriage problem is a well-known problem of matching men to women so that no man and woman, who are not married to each other, both prefer each other. Such a problem has a wide variety of practical applications, ranging from…
The stable roommates problem is a non-bipartite version of the stable matching problem in a bipartite graph. In this paper, we consider the stable roommates problem with ties. In particular, we focus on strong stability, which is one of the…
We thoroughly study a generalized version of the classic Stable Marriage and Stable Roommates problems where agents may share partners. We consider two prominent stability concepts: ordinal stability [Aharoni and Fleiner, Journal of…
A probabilistic approach to the stable matching problem has been identified as an important research area with several important open problems. When considering random matchings, ex-post stability is a fundamental stability concept. A…
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…
We study control problems in the context of matching under preferences: We examine how a central authority, called the controller, can manipulate an instance of the Stable Marriage or Stable Roommates problems in order to achieve certain…
This paper studies the Nash stability in hedonic coalition formation games. We address the following issue: for a general problem formulation, is there any utility allocation method ensuring a Nash-stable partition? We propose the…
The classic Stable Roommates problem (which is the non-bipartite generalization of the well-known Stable Marriage problem) asks whether there is a stable matching for a given set of agents, i.e. a partitioning of the agents into disjoint…
We study how stability can be maintained even after any set of at most k players leave their groups, in the context of hedonic games. While stability properties ensure an outcome to be robust against players' deviations, it has not been…
A well known result states that stability criterion for matchings in two-sided markets doesn't ensure uniqueness. This opens the door for a moral question with regard to the optimal stable matching from a social point of view. Here, a new…
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…