Related papers: Unique Stable Matchings
I relate bipartite graph matchings to stable matchings. I prove a necessary and sufficient condition for the existence of a saturating stable matching, where every agent on one side is matched, for all possible preferences. I extend my…
This paper focuses on two-sided matching where one side (a hospital or firm) is matched to the other side (a doctor or worker) so as to maximize a cardinal objective under general feasibility constraints. In a standard model, even though…
In many empirical studies of a large two-sided matching market (such as in a college admissions problem), the researcher performs statistical inference under the assumption that they observe a random sample from a large matching market. In…
We study the stable matching problem in non-bipartite graphs with incomplete but strict preference lists, where the edges have weights and the goal is to compute a stable matching of minimum or maximum weight. This problem is known to be…
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…
Given $n$ men, $n$ women, and $n$ dogs, each man has an incomplete preference list of women, each woman does an incomplete preference list of dogs, and each dog does an incomplete preference list of men. We understand a family as a triple…
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…
Shapley and Scarf introduced a notion of stable allocation between traders and indivisible goods, when each trader has rank-ordered each of the goods. The purpose of this note is to prove that the distribution of ranks after allocation is…
Let each point of a homogeneous Poisson process on $\RR$ independently be equipped with a random number of stubs (half-edges) according to a given probability distribution $\mu$ on the positive integers. We consider schemes based on…
This paper proposes a new one-sided matching market model in which every agent has a cost function that is allowed to take a negative value. Our model aims to capture the situation where some agents can profit by exchanging their obtained…
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…
This paper develops a method to use singles' data in a non-parametric revealed preference setting of collective household choice. We use it to test the controversial assumption of preference stability between singles and couples, without…
Efficient computability is an important property of solution concepts in matching markets. We consider the computational complexity of finding and verifying various solution concepts in trading networks-multi-sided matching markets with…
The assignment game models a housing market where buyers and sellers are matched, and transaction prices are set so that the resulting allocation is stable. Shapley and Shubik showed that every stable allocation is necessarily built on a…
This paper characterizes equilibrium properties of a broad class of economic models that allow multiple heterogeneous agents to interact in heterogeneous manners across several markets. Our key contribution is a new theorem providing…
In economics and social choice single-peakedness is one of the most important and commonly studied models for preferences. It is well known that single-peaked consistency for total orders is in P. However in practice a preference profile is…
In the housing market model introduced by Shapley and Scarf (1974), we propose a new axiom, local unanimity, that extends the unanimity condition widely used in social choice theory. It applies the unanimity condition to any subset 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…
Suppose that red and blue points occur as independent homogeneous Poisson processes in R^d. We investigate translation-invariant schemes for perfectly matching the red points to the blue points. For any such scheme in dimensions d=1,2, the…
This paper examines equilibria in dynamic two-sided matching games, extending Gale and Shapley's foundational model to a non-cooperative, decentralized, and dynamic framework. We focus on markets where agents have utility functions and…