Related papers: Stable Marriage with One-Sided Preference
This study considers a model where schools may have multiple priority orders on students, which may be inconsistent with each other. For example, in school choice systems, since the sibling priority and the walk zone priority coexist, the…
The \textsc{Housing Market} problem is a widely studied resource allocation problem. In this problem, each agent can only receive a single object and has preferences over all objects. Starting from an initial endowment, we want to reach a…
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…
In many matching markets, one side "applies" to the other, and these applications are often expensive and time-consuming (e.g. students applying to college). It is tempting to think that making the application process easier should benefit…
The many-to-one stable matching problem provides the fundamental abstraction of several real-world matching markets such as school choice and hospital-resident allocation. The agents on both sides are often referred to as residents and…
In the theory of two-sided matching markets there are two well-known models: the marriage model (where no money is involved) and the assignment model (where payments are involved). Roth and Sotomayor (1990) asked for an explanation for the…
This paper develops an integer programming approach to two-sided many-to-one matching by investigating stable integral matchings of a fictitious market where each worker is divisible. We show that stable matchings exist in a discrete…
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…
Reallocating resources to get mutually beneficial outcomes is a fundamental problem in various multi-agent settings. While finding an arbitrary Pareto optimal allocation is generally easy, checking whether a particular allocation is Pareto…
Two-sided matching markets have long existed to pair agents in the absence of regulated exchanges. A common example is school choice, where a matching mechanism uses student and school preferences to assign students to schools. In such…
In this study, we consider the real-world problem of assigning students to classes, where each student has a preference list, ranking a subset of classes in order of preference. Though we use existing approaches to include the daily class…
We propose a pseudo-market solution to resource allocation problems subject to constraints. Our treatment of constraints is general: including bihierarchical constraints due to considerations of diversity in school choice, or scheduling in…
Prevailing methods of course allocation at undergraduate institutions involve reserving seats to give priority to designated groups of students. We introduce a competitive equilibrium-based mechanism that assigns course seats using student…
Consider the group of $n$ men and $n$ women, each with their own preference list for a potential marriage partner. The stable marriage is a bipartite matching such that no unmatched pair (man, woman) prefer each other to their partners in…
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…
We introduce a new and broader formulation of the stable marriage problem (SMP), called the stable polygamy problem (SPP), where multiple individuals from a larger group $L$ of $|L|$ individuals can be matched with a single individual from…
We study the problem of pure exploration in matching markets under uncertain preferences, where the goal is to identify a stable matching with confidence parameter $\delta$ and minimal sample complexity. Agents learn preferences via…
This paper studies a matching problem in which a group of agents cooperate with agents on two sides. In environments with either nontransferable or transferable utilities, we demonstrate that a stable outcome exists when cooperations…
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,…
This note proposes a simple polynomial-time method for constructing an ex ante stable school-choice lottery satisfying equal treatment of equals. The method applies the ETE reassignment to a constrained efficient stable matching and yields…