scholarly journals Pairwise Stable Matching in Large Economies

Econometrica ◽  
2021 ◽  
Vol 89 (6) ◽  
pp. 2929-2974 ◽  
Author(s):  
Michael Greinecker ◽  
Christopher Kah
Keyword(s):  
General Class ◽  
Stable Matching ◽  
High Dimensional ◽  
Transferable Utility ◽  
Stable Matchings ◽  
Matching Problems ◽  
Joint Distributions ◽  
Special Cases ◽  
Matching Models ◽  
Stability Notions

We formulate a stability notion for two‐sided pairwise matching problems with individually insignificant agents in distributional form. Matchings are formulated as joint distributions over the characteristics of the populations to be matched. Spaces of characteristics can be high‐dimensional and need not be compact. Stable matchings exist with and without transfers, and stable matchings correspond precisely to limits of stable matchings for finite‐agent models. We can embed existing continuum matching models and stability notions with transferable utility as special cases of our model and stability notion. In contrast to finite‐agent matching models, stable matchings exist under a general class of externalities.

Matching under Transferable Utility: Some Extensions

2017 ◽  
Author(s):  
Pierre-André Chiappori
Keyword(s):  
Human Capital ◽  
Risk Sharing ◽  
Marriage Market ◽  
Stable Matching ◽  
Coase Theorem ◽  
Transferable Utility ◽  
Matching Problem ◽  
Basic Model ◽  
Matching Models ◽  
Roommate Matching

This chapter considers some extensions of matching models under transferable utility (TU). It begins with a discussion of preinvestment, in which agents deliberately invest in education, and the stock of human capital that characterizes them when entering the marriage market is therefore (at least partly) endogenous. It is safe to assume that agents, when deciding their investment, take into account, among other things, its impact on the marriage market. An alternative argument is that agents are likely to invest too much. The chapter proceeds by analyzing the relevance of TU to risk sharing, multidimensional matching, and the roommate matching problem, taking into account the existence of a stable matching and the cloned bipartite problem. Finally, it describes the basic model of divorce and remarriage, focusing on compensations in the Becker-Coase theorem as well as violations of the theorem.

scholarly journals Rate of Convergence for Ibragimov-Gadjiev-Durrmeyer Operators

2017 ◽  
Vol 50 (1) ◽  
pp. 119-129 ◽  
Author(s):  
Tuncer Acar
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
General Class ◽  
Durrmeyer Operators ◽  
Special Cases ◽  
Derivatives Of

Abstract The present paper deals with the rate of convergence of the general class of Durrmeyer operators, which are generalization of Ibragimov-Gadjiev operators. The special cases of the operators include somewell known operators as particular cases viz. Szász-Mirakyan-Durrmeyer operators, Baskakov-Durrmeyer operators. Herewe estimate the rate of convergence of Ibragimov-Gadjiev-Durrmeyer operators for functions having derivatives of bounded variation.

scholarly journals CMPH: a multivariate phase-type aggregate loss distribution

2017 ◽  
Vol 5 (1) ◽  
pp. 304-315 ◽  
Author(s):  
Jiandong Ren ◽  
Ricardas Zitikis
Keyword(s):  
Negative Binomial ◽  
Risk Measures ◽  
Moment Generating Function ◽  
Insurance Companies ◽  
Joint Distributions ◽  
Special Cases ◽  
Risk Sources ◽  
Computational Aspects ◽  
Aggregate Loss ◽  
Aggregate Loss Distribution

AbstractWe introduce a compound multivariate distribution designed for modeling insurance losses arising from different risk sources in insurance companies. The distribution is based on a discrete-time Markov Chain and generalizes the multivariate compound negative binomial distribution, which is widely used for modeling insurance losses.We derive fundamental properties of the distribution and discuss computational aspects facilitating calculations of risk measures of the aggregate loss, as well as allocations of the aggregate loss to individual types of risk sources. Explicit formulas for the joint moment generating function and the joint moments of different loss types are derived, and recursive formulas for calculating the joint distributions given. Several special cases of particular interest are analyzed. An illustrative numerical example is provided.

Stable Matching with Double Infinity of Workers and Firms

2018 ◽  
Vol 19 (2) ◽  
Author(s):  
Matías Fuentes ◽  
Fernando Tohmé
Keyword(s):  
Stable Matching ◽  
Pareto Optimal ◽  
Stable Matchings ◽  
Large Market ◽  
Countably Infinite

Abstract In this paper we analyze the existence of stable matchings in a two-sided large market in which workers are assigned to firms. The market has a continuum of workers while the set of firms is countably infinite. We show that, under certain reasonable assumptions on the preference correspondences, stable matchings not only exist but are also Pareto optimal.

Near-Feasible Stable Matchings with Couples

2018 ◽  
Vol 108 (11) ◽  
pp. 3154-3169 ◽  
Author(s):  
Thành Nguyen ◽  
Rakesh Vohra
Keyword(s):  
Medical Students ◽  
Stable Matching ◽  
Teaching Hospitals ◽  
Matching Problem ◽  
Stable Matchings ◽  
Student Preferences

The National Resident Matching program seeks a stable matching of medical students to teaching hospitals. With couples, stable matchings need not exist. Nevertheless, for any student preferences, we show that each instance of a matching problem has a “nearby” instance with a stable matching. The nearby instance is obtained by perturbing the capacities of the hospitals. In this perturbation, aggregate capacity is never reduced and can increase by at most four. The capacity of each hospital never changes by more than two. (JEL C78, D47, I11, J41, J44)

scholarly journals Adapting Stable Matchings to Evolving Preferences

2020 ◽  
Vol 34 (02) ◽  
pp. 1830-1837 ◽  
Author(s):  
Robert Bredereck ◽  
Jiehua Chen ◽  
Dušan Knop ◽  
Junjie Luo ◽  
Rolf Niedermeier
Keyword(s):  
Computational Complexity ◽  
Computational Cost ◽  
Modern Society ◽  
Stable Matching ◽  
Stable Marriage ◽  
Fixed Parameter Tractability ◽  
Stable Matchings ◽  
Changing Environments ◽  
Fixed Parameter ◽  
Comprehensive Picture

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 both problems, what is the computational cost of adapting an existing stable matching after some of the preferences of the agents have changed. While doing so, we also model the constraint that the new stable matching shall be not too different from the old one. After formalizing these incremental versions, we provide a fairly comprehensive picture of the computational complexity landscape of Incremental Stable Marriage and Incremental Stable Roommates. To this end, we exploit the parameters “degree of change” both in the input (difference between old and new preference profile) and in the output (difference between old and new stable matching). We obtain both hardness and tractability results, in particular showing a fixed-parameter tractability result with respect to the parameter “distance between old and new stable matching”.

scholarly journals Multiensemble Markov models of molecular thermodynamics and kinetics

2016 ◽  
Vol 113 (23) ◽  
pp. E3221-E3230 ◽  
Author(s):  
Hao Wu ◽  
Fabian Paul ◽  
Christoph Wehmeyer ◽  
Frank Noé
Keyword(s):  
Detailed Balance ◽  
Rare Event ◽  
Umbrella Sampling ◽  
High Dimensional ◽  
Acceptance Ratio ◽  
Markov State ◽  
Markov State Models ◽  
Bennett Acceptance Ratio ◽  
Special Cases ◽  
State Models

We introduce the general transition-based reweighting analysis method (TRAM), a statistically optimal approach to integrate both unbiased and biased molecular dynamics simulations, such as umbrella sampling or replica exchange. TRAM estimates a multiensemble Markov model (MEMM) with full thermodynamic and kinetic information at all ensembles. The approach combines the benefits of Markov state models—clustering of high-dimensional spaces and modeling of complex many-state systems—with those of the multistate Bennett acceptance ratio of exploiting biased or high-temperature ensembles to accelerate rare-event sampling. TRAM does not depend on any rate model in addition to the widely used Markov state model approximation, but uses only fundamental relations such as detailed balance and binless reweighting of configurations between ensembles. Previous methods, including the multistate Bennett acceptance ratio, discrete TRAM, and Markov state models are special cases and can be derived from the TRAM equations. TRAM is demonstrated by efficiently computing MEMMs in cases where other estimators break down, including the full thermodynamics and rare-event kinetics from high-dimensional simulation data of an all-atom protein–ligand binding model.

Matching under Transferable Utility: Applications

2017 ◽  
Author(s):  
Pierre-André Chiappori
Keyword(s):  
Higher Education ◽  
Birth Control ◽  
Marriage Market ◽  
Comparative Statics ◽  
Female Empowerment ◽  
Control Technology ◽  
Transferable Utility ◽  
Male And Female ◽  
Roe V Wade ◽  
Matching Models

This chapter considers two examples of applications of matching models under transferable utility (TU). The first example deals with the legalization of abortion by virtue of Roe v. Wade and the feminist claim that it empowered all women. The second example deals with the discrepancy between male and female demand for higher education over the last decades. After providing an overview of Roe v. Wade and how it resulted in female empowerment, the chapter describes the model that takes into account preferences and budget constraints, stable matching on the marriage market, and changes in birth control technology. It then examines gender differences in the demand for higher education using the CIW (Chiappori, Iyigun, and Weiss) model, with a focus on equilibrium, preferences for singlehood, comparative statics, empirical implementation, and the Low model showing that higher education results in a deterministic drop in fertility.

scholarly journals Estimation and filtering of fractional generalised random fields

2000 ◽  
Vol 69 (3) ◽  
pp. 336-361 ◽  
Author(s):  
J. M. Angulo ◽  
M. D. Ruiz-Medina ◽  
V. V. Anh
Keyword(s):  
Brownian Motion ◽  
Random Field ◽  
Least Squares ◽  
Random Fields ◽  
General Class ◽  
Duality Theory ◽  
Weak Sense ◽  
Linear Estimation ◽  
Special Cases ◽  
Estimation And Filtering

AbstractThis paper considers the estimation and filtering of fractional random fields, of which fractional Brownian motion and fractional Riesz-Bessel motion are important special cases. A least-squares solution to the problem is derived by using the duality theory and covariance factorisation of fractional generalised random fields. The minimum fractional duality order of the information random field leads to the most general class of solutions corresponding to the largest function space where the output random field can be approximated. The second-order properties that define the class of random fields for which the least-squares linear estimation problem is solved in a weak-sense are also investigated in terms of the covariance spectrum of the information random field.

scholarly journals Optimal errors and phase transitions in high-dimensional generalized linear models

2019 ◽  
Vol 116 (12) ◽  
pp. 5451-5460 ◽  
Author(s):  
Jean Barbier ◽  
Florent Krzakala ◽  
Nicolas Macris ◽  
Léo Miolane ◽  
Lenka Zdeborová
Keyword(s):  
Phase Transitions ◽  
Generalized Linear Models ◽  
Message Passing ◽  
Statistical Physics ◽  
Linear Models ◽  
Optimal Estimation ◽  
Error Correcting Codes ◽  
Data Matrix ◽  
High Dimensional ◽  
Special Cases

Generalized linear models (GLMs) are used in high-dimensional machine learning, statistics, communications, and signal processing. In this paper we analyze GLMs when the data matrix is random, as relevant in problems such as compressed sensing, error-correcting codes, or benchmark models in neural networks. We evaluate the mutual information (or “free entropy”) from which we deduce the Bayes-optimal estimation and generalization errors. Our analysis applies to the high-dimensional limit where both the number of samples and the dimension are large and their ratio is fixed. Nonrigorous predictions for the optimal errors existed for special cases of GLMs, e.g., for the perceptron, in the field of statistical physics based on the so-called replica method. Our present paper rigorously establishes those decades-old conjectures and brings forward their algorithmic interpretation in terms of performance of the generalized approximate message-passing algorithm. Furthermore, we tightly characterize, for many learning problems, regions of parameters for which this algorithm achieves the optimal performance and locate the associated sharp phase transitions separating learnable and nonlearnable regions. We believe that this random version of GLMs can serve as a challenging benchmark for multipurpose algorithms.

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