Related papers: Three-Dimensional Popular Matching with Cyclic Pre…
Coalition formation over graphs is a well studied class of games whose players are vertices and feasible coalitions must be connected subgraphs. In this setting, the existence and computation of equilibria, under various notions of…
It is well known that every stable matching instance $I$ has a rotation poset $R(I)$ that can be computed efficiently and the downsets of $R(I)$ are in one-to-one correspondence with the stable matchings of $I$. Furthermore, for every poset…
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…
We use the indirect evolutionary approach to study evolutionarily stable preferences against multiple mutations in single- and multi-population matching settings, respectively. Players choose strategies to maximize their subjective…
The literature on centralized matching markets often assumes that a true preference of each player is known to herself and fixed, but empirical evidence casts doubt on its plausibility. To circumvent the problem, we consider evolutionary…
Research regarding the stable marriage and roommate problem has a long and distinguished history in mathematics, computer science and economics. Stability in this context is predominantly core stability or one of its variants in which each…
We introduce a new algorithm for finding stable matchings in multi-sided matching markets. Our setting is motivated by a PhD market of students, advisors, and co-advisors, and can be generalized to supply chain networks viewed as $n$-sided…
Given a set $A$ of $n$ people and a set $B$ of $m \geq n$ items, with each person having a list that ranks his/her preferred items in order of preference, we want to match every person with a unique item. A matching $M$ is called popular if…
A preference system $\mathcal{I}$ is an undirected graph where vertices have preferences over their neighbors, and $\mathcal{I}$ admits a master list if all preferences can be derived from a single ordering over all vertices. We study the…
Suppose that each member of a set of agents has a preference list of a subset of houses, possibly involving ties and each agent and house has their capacity denoting the maximum number of correspondingly agents/houses that can be matched to…
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…
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…
Variational stability, in the sense of local good behavior of optimal values and solutions in problems of optimization under shifts in parameters, is important not only for validating model robustness in practical applications but also for…
This paper studies matching markets where institutions are matched with possibly more than one individual. The matching market contains some couples who view the pair of jobs as complements. First, we show by means of an example that a…
Random embeddings project high-dimensional spaces to low-dimensional ones; they are careful constructions which allow the approximate preservation of key properties, such as the pair-wise distances between points. Often in the field of…
This paper focuses on two-sided matching where one side (a hospital or firm) is matched to the other side (a doctor or worker) so as to maximize a cardinal objective under general feasibility constraints. In a standard model, even though…
We study the 3D-Euclidean Multidimensional Stable Roommates problem, which asks whether a given set $V$ of $s\cdot n$ agents with a location in 3-dimensional Euclidean space can be partitioned into $n$ disjoint subsets $\pi = \{R_1 ,\dots ,…
Stable matchings have been studied extensively in social choice literature. The focus has been mostly on integral matchings, in which the nodes on the two sides are wholly matched. A fractional matching, which is a convex combination of…
Let $G$ be a bipartite graph where every node has a strict ranking of its neighbors. For every node, its preferences over neighbors extend naturally to preferences over matchings. Matching $N$ is more popular than matching $M$ if the number…
In this paper we consider stable matchings subject to assignment constraints. These are matchings that require certain assigned pairs to be included, insist that some other assigned pairs are not, and, importantly, are stable. Our main…