Related papers: Stability in Many-to-One Matching with Couples hav…
We study the stable marriage problem from different points of view. We proposed a microscopic dynamic that lead the system to a stationary state that we are able to characterize analytically. Then, we derive a thermodynamical description of…
Robust Stable Marriage (RSM) is a variant of the classical Stable Marriage problem, where the robustness of a given stable matching is measured by the number of modifications required for repairing it in case an unforeseen event occurs. We…
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 rise of Large Language Models (LLMs) has driven progress in reasoning tasks -- from program synthesis to scientific hypothesis generation -- yet their ability to handle ranked preferences and structured algorithms in combinatorial…
Gale and Shapley introduced a matching problem between two sets of agents where each agent on one side has an exogenous preference ordering over the agents on the other side. They defined a matching as stable if no unmatched pair can both…
To guarantee all agents are matched in general, the classic Deferred Acceptance algorithm needs complete preference lists. In practice, preference lists are short, yet stable matching still works well. This raises two questions: $\bullet$…
This paper considers two-sided matching with budget constraints where one side (firm or hospital) can make monetary transfers (offer wages) to the other (worker or doctor). In a standard model, while multiple doctors can be matched to a…
For most people, social contacts play an integral part in finding a new job. As observed by Granovetter's seminal study, the proportion of jobs obtained through social contacts is usually large compared to those obtained through postings or…
For a many-to-many matching market, we study the lattice structure of the set of random stable matchings. We define a partial order on the random stable set and present two intuitive binary operations to compute the least upper bound and…
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…
In the {\sc Course Allocation} problem, there are a set of students and a set of courses at a given university. University courses may have different numbers of credits, typically related to different numbers of learning hours, and there…
In many two-sided labor markets, interviews are conducted before matches are formed. The growing number of interviews in medical residency markets has increased demand for signaling mechanisms, where applicants send a limited number of…
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 study a many-to-one matching problem, such as the college admission problem, where each college can admit multiple students. Unlike classical models, colleges evaluate sets of students through non-linear utility functions that capture…
We develop inference for a two-sided matching model where the characteristics of agents on one side of the market are endogenous due to pre-matching investments. The model can be used to measure the impact of frictions in labour markets…
Stable matching is a fundamental problem studied both in economics and computer science. The task is to find a matching between two sides of agents that have preferences over who they want to be matched with. A matching is stable if no pair…
In many centralized labor markets candidates interview with potential employers before matches are formed through a clearinghouse One prominent example is the market for medical residencies and fellowships, which in recent years has had a…
We study the competition for partners in two-sided matching markets with heterogeneous agent preferences, with a focus on how the equilibrium outcomes depend on the connectivity in the market. We model random partially connected markets,…
We study a variant of the Student-Project Allocation problem with lecturer preferences over Students where ties are allowed in the preference lists of students and lecturers (SPA-ST). We investigate the concept of strong stability in this…
Properties of stable matchings in the popular random-matching-market model have been studied for over 50 years. In a random matching market, each agent has complete preferences drawn uniformly and independently at random. Wilson (1972),…