Related papers: Scaling Behavior in the Stable Marriage Problem
In this paper we consider the problem of finding an evolution of a dynamical system that originates and terminates in given sets of states. However, if such an evolution exists then it is usually not unique. We investigate this problem and…
We study the problem of capacity modification in the many-to-one stable matching of workers and firms. Our goal is to systematically study how the set of stable matchings changes when some seats are added to or removed from the firms. We…
We study stability notions for networked many-to-many matching markets with individually insignificant agents in distributional form. Outcomes are formulated as joint distributions over characteristics of agents and contract choices.…
Motivated by growing evidence of agents' mistakes in strategically simple environments, we propose a solution concept -- robust equilibrium -- that requires only an asymptotically optimal behavior. We use it to study large random matching…
The maximal matching problem has received considerable attention in the self-stabilizing community. Previous work has given different self-stabilizing algorithms that solves the problem for both the adversarial and fair distributed daemon,…
In a dynamic matching market, such as a marriage or job market, how should agents balance accepting a proposed match with the cost of continuing their search? We consider this problem in a discrete setting, in which agents have cardinal…
Estimation of the population total of a variable can be improved by calibration on a set of auxiliary variables. It is difficult to establish that such a set of variables is sufficient, that estimation could not be improved by calibration…
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…
Conditional stability estimates allow us to characterize the degree of ill-posedness of many inverse problems, but without further assumptions they are not sufficient for the stable solution in the presence of data perturbations. We here…
We study variants of the stable marriage and college admissions models in which the agents are allowed to express weak preferences over the set of agents on the other side of the market and the option of remaining unmatched. For the…
A probabilistic approach to the stable matching problem has been identified as an important research area with several important open problems. When considering random matchings, ex-post stability is a fundamental stability concept. A…
Many important stable matching problems are known to be NP-hard, even when strong restrictions are placed on the input. In this paper we seek to identify structural properties of instances of stable matching problems which will allow us to…
A basic requirement for a mathematical model is often that its solution (output) shouldn't change much if the model's parameters (input) are perturbed. This is important because the exact values of parameters may not be known and one would…
In this paper, I characterize minimal stable voting rules and minimal self-stable constitutions (i.e., pairs of voting rules) for societies in which only power matters. To do so, I first let players' preference profiles over voting rules…
Feedback optimization refers to a class of methods that steer a control system to a steady state that solves an optimization problem. Despite tremendous progress on the topic, an important problem remains open: enforcing state constraints…
Large language models with a huge number of parameters, when trained on near internet-sized number of tokens, have been empirically shown to obey neural scaling laws: specifically, their performance behaves predictably as a power law in…
We study the problem of finding solutions to the stable matching problem that are robust to errors in the input and we obtain a polynomial time algorithm for a special class of errors. In the process, we also initiate work on a new…
The stable marriage problem with ties is a well-studied and interesting problem in game theory. We are given a set of men and a set of women. Each individual has a preference ordering on the opposite group, which can possibly contain ties.…
Stability selection is a widely adopted resampling-based framework for high-dimensional variable selection. This paper seeks to broaden the use of an established stability estimator to evaluate the overall stability of the stability…
Optimization under uncertainty deals with the problem of optimizing stochastic cost functions given some partial information on their inputs. These problems are extremely difficult to solve and yet pervade all areas of technological and…