Related papers: Roommates with Convex Preferences
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…
We study stable matching problems where agents have multilayer preferences: There are $\ell$ layers each consisting of one preference relation for each agent. Recently, Chen et al. [EC '18] studied such problems with strict preferences,…
We consider the problem of finding Pareto-optimal allocations of risk among finitely many agents. The associated individual risk measures are law invariant, but with respect to agent-dependent and potentially heterogeneous reference…
We consider the optimal risk sharing problem with a continuum of agents, modeled via a non-atomic measure space. Individual preferences are not assumed to be convex. We show the multiplicity of agents induces the value function to be…
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…
Selecting a set of alternatives based on the preferences of agents is an important problem in committee selection and beyond. Among the various criteria put forth for the desirability of a committee, Pareto optimality is a minimal and…
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…
We are given a bipartite graph $G = \left( A \cup B, E \right)$. In the one-sided model, every $a \in A$ (often called agents) ranks its neighbours $z \in N_{a}$ strictly, and no $b \in B$ has any preference order over its neighbours $y \in…
We study the classical, two-sided stable marriage problem under pairwise preferences. In the most general setting, agents are allowed to express their preferences as comparisons of any two of their edges and they also have the right to…
We analyze the problem of locating a public facility in a domain of single-peaked and single-dipped preferences when the social planner knows the type of preference (single-peaked or single-dipped) of each agent. Our main result…
Suppose each of $n$ men and $n$ women is located at a point in a metric space. A woman ranks the men in order of their distance to her from closest to farthest, breaking ties at random. The men rank the women similarly. An interesting…
The stable marriage problem has been introduced in order to describe a complex system where individuals attempt to optimise their own satisfaction, subject to mutually conflicting constraints. Due to the potential large applicability of…
Most prior work on online matching problems has been with the flexibility of keeping some vertices unmatched. We study three related online matching problems with the constraint of matching every vertex, i.e., with no rejections. We adopt a…
In a dynamic matching market, such as a marriage or job market, how should agents balance accepting a proposed match with the cost of continuing their search? We consider this problem in a discrete setting, in which agents have cardinal…
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…
An input to the Popular Matching problem, in the roommates setting, consists of a graph $G$ and each vertex ranks its neighbors in strict order, known as its preference. In the Popular Matching problem the objective is to test whether there…
In many matching markets--such as athlete recruitment or academic admissions--participants on one side are evaluated by attribute vectors known to the other side, which in turn applies individual \emph{salience vectors} to assign relative…
In a multiple partners matching problem the agents can have multiple partners up to their capacities. In this paper we consider both the two-sided many-to-many stable matching problem and the one-sided stable fixtures problem under…
We revisit the problem of designing optimal, individually rational matching mechanisms (in a general sense, allowing for cycles in directed graphs), where each player --- who is associated with a subset of vertices --- matches as many of…
A group of $n$ agents with numerical preferences for each other are to be assigned to the $n$ seats of a dining table. We study two natural topologies:~circular (cycle) tables and panel (path) tables. For a given seating arrangement, an…