Related papers: Characterizing Stability in Many-to-One Matching w…
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…
In stable matching, one must find a matching between two sets of agents, commonly men and women, or job applicants and job positions. Each agent has a preference ordering over who they want to be matched with. Moreover a matching is said to…
We consider a variant of socially stable marriage problem where preference lists may be incomplete, may contain ties and may have bounded length. In real world application like NRMP and Scottish medical matching scheme such restrictions…
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…
The classical stable marriage problem asks for a matching between a set of men and a set of women with no blocking pairs, which are pairs formed by a man and a woman who would both prefer switching from their current status to be paired up…
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…
Consider a cyclically ordered collection of $r$ equinumerous agent sets with strict preferences of every agent over the agents from the next agent set. A weakly stable cyclic matching is a partition of the set of agents into disjoint union…
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…
The stable matching problem sets the economic foundation of several practical applications ranging from school choice and medical residency to ridesharing and refugee placement. It is concerned with finding a matching between two disjoint…
In this paper we show that when individuals in a bipartite network exclusively choose partners and exchange valued goods with their partners, then there exists a set of exchanges that are pair-wise stable. Pair-wise stability implies that…
We consider many-to-one matching problems, where one side corresponds to applicants who have preferences and the other side to houses who do not have preferences. We consider two different types of this market: one, where the applicants…
In a many-to-one matching market, we analyze the matching game induced by a stable rule when firms' choice function satisfy substitutability. We show that any stable rule implements the individually rational correspondence in Nash…
We investigate in this paper the theory and econometrics of optimal matchings with competing criteria. The surplus from a marriage match, for instance, may depend both on the incomes and on the educations of the partners, as well as on…
We study dynamic decentralized two-sided matching in which players may encounter unanticipated experiences. As they become aware of these experiences, they may change their preferences over players on the other side of the market.…
The matching hypothesis in social psychology claims that people are more likely to form a committed relationship with someone equally attractive. Previous works on stochastic models of human mate choice process indicate that patterns…
In a many-to-many matching model in which agents' preferences satisfy substitutability and the law of aggregate demand, we present an algorithm to compute the full set of stable matchings. This algorithm relies on the idea of "cycles in…
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…
For a many-to-one matching model, we study the matchings obtained through the restabilization of stable matchings that had been disrupted by a change in the population. We include a simple representation of the stable matching obtained in…
Pairwise model comparisons drawn from foundation-model benchmarks ("A is safer than B") are read as quantitative verdicts but hinge on harness choices benchmark papers under-specify. We close one theory-benchmark loop on this primitive: a…
We study the design of one-to-one matching mechanisms that are strategy-proof for both sides and as stable as possible. Motivated by the impossibility result of Roth (1982), we formulate the mechanism design problem as a linear program that…