Related papers: Stable Matching with Uncertain Linear Preferences
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…
Stable matching is a fundamental area with many practical applications, such as centralised clearinghouses for school choice or job markets. Recent work has introduced the paradigm of near-feasibility in capacitated matching settings, where…
In the Stable Marriage problem. when the preference lists are complete, all agents of the smaller side can be matched. However, this need not be true when preference lists are incomplete. In most real-life situations, where agents…
Colloquially, there are two groups, $n$ men and $n$ women, each man (woman) ranking women (men) as potential marriage partners. A complete matching is called stable if no unmatched pair prefer each other to their partners in the matching.…
This paper links matching markets with aligned preferences to optimal transport theory. We show that stability, efficiency, and fairness emerge as solutions to a parametric family of optimal transport problems. The parameter reflects…
In this paper we consider the issue of a unique prediction in one to one two sided matching markets, as defined by Gale and Shapley (1962), and we prove the following. Theorem. Let P be a one-to-one two-sided matching market and let P be…
Assume that $n = 2k$ potential roommates each have an ordered preference of the $n-1$ others. A stable matching is a perfect matching of the $n$ roommates in which no two unmatched people prefer each other to their matched partners. In…
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…
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.…
Recent studies on many-to-one matching markets have explored agents with flexible capacity and truthful preference reporting, focusing on mechanisms that jointly design capacities and select a matching. However, in real-world applications…
Adaptivity to changing environments and constraints is key to success in modern society. We address this by proposing "incrementalized versions" of Stable Marriage and Stable Roommates. That is, we try to answer the following question: for…
We consider stable three-dimensional matchings of three categories of agents, such as women, men and dogs. This was suggested long ago by Knuth (1976), but very little seems to have been published on this problem. Based on computer…
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…
In the stable marriage problem N men and N women have to be matched by pairs under the constraint that the resulting matching is stable. We study the statistical properties of stable matchings in the large N limit using both numerical and…
The stable roommates problem is a non-bipartite version of the stable matching problem in a bipartite graph. In this paper, we consider the stable roommates problem with ties. In particular, we focus on strong stability, which is one of the…
It is well known that a stable matching in a many-to-one matching market with couples need not exist. We introduce a new matching algorithm for such markets and show that for a general class of large random markets the algorithm will find 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…
We consider a two-sided matching problem in which the agents on one side have dichotomous preferences and the other side representing institutions has strict preferences (priorities). It captures several important applications in matching…
In this paper we consider multi-agent coalitional games with uncertain value functions for which we establish distribution-free guarantees on the probability of allocation stability, i.e., agents do not have incentives to defect from the…
An approximation of strategyproofness in large, two-sided matching markets is highly evident. Through simulations, one can observe that the percentage of agents with useful deviations decreases as the market size grows. Furthermore, there…