Matching with Transfers: Basic Notions

2017 ◽  
Author(s):  
Pierre-André Chiappori
Keyword(s):  
Metric Spaces ◽  
Transferable Utility ◽  
Equilibrium Concept ◽  
Matching Problem ◽  
Basic Equilibrium ◽  
One To One ◽  
Definition Of ◽  
Matching Models

This chapter describes the basic notions of matching with transfers. It first introduces the notations that will be used throughout the book, including two compact, separable metric spaces: the space of female characteristics and the space of male characteristics. In particular, it outlines a framework that is common to all (bipartite, one-to-one) matching models. It then considers how a matching problem is defined in the nontransferable utility, transferable utility, and imperfectly transferable utility cases. It also explains how the solution is defined in all three cases, noting that there are differences in the definition of an equilibrium. In all cases, the basic equilibrium concept is stability.

Matching under Transferable Utility: Theory

2017 ◽  
Author(s):  
Pierre-André Chiappori
Keyword(s):  
Pareto Frontier ◽  
Intrahousehold Allocation ◽  
Formal Definition ◽  
Hedonic Models ◽  
Transferable Utility ◽  
Property A ◽  
Hedonic Equilibrium ◽  
Definition Of ◽  
Matching Models ◽  
The Relationship

This chapter considers the theory of matching under transferable utility (TU). It first introduces a formal definition of the TU property: a group satisfies TU if there exists monotone transformations of individual utilities such that the Pareto frontier is a hyperplane. It then examines the cornerstone of the theory of nontransferable utility (NTU) matching, namely, the Gale-Shapley algorithm, before turning to a discussion of a crucial property of matching models under TU: their intrinsic relationship with optimal transportation. It also describes the notions of supermodularity and assortativeness, along with individual utilities and intrahousehold allocation. Finally, it looks at hedonic models, taking into account hedonic equilibrium and stable matching, and presents two examples that illustrate the relationship between matching and hedonic models: a competitive IO model and randomized matching.

scholarly journals The Econometrics and Some Properties of Separable Matching Models

2017 ◽  
Vol 107 (5) ◽  
pp. 251-255 ◽  
Author(s):  
Alfred Galichon ◽  
Bernard Salanié
Keyword(s):  
Comparative Statics ◽  
Transferable Utility ◽  
Separable Models ◽  
One To One ◽  
Matching Models

We present a class of one-to-one matching models with perfectly transferable utility. We discuss identification and inference in these separable models, and we show how their comparative statics are readily analyzed.

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 Fixed Point of Interpolative Rus–Reich–Ćirić Contraction Mapping on Rectangular Quasi-Partial b-Metric Space

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 32
Author(s):  
Pragati Gautam ◽  
Luis Manuel Sánchez Ruiz ◽  
Swapnil Verma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Real Number ◽  
Metric Space ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Rectangular Metric Space ◽  
New Type ◽  
Symmetry Requirement ◽  
Definition Of

The purpose of this study is to introduce a new type of extended metric space, i.e., the rectangular quasi-partial b-metric space, which means a relaxation of the symmetry requirement of metric spaces, by including a real number s in the definition of the rectangular metric space defined by Branciari. Here, we obtain a fixed point theorem for interpolative Rus–Reich–Ćirić contraction mappings in the realm of rectangular quasi-partial b-metric spaces. Furthermore, an example is also illustrated to present the applicability of our result.

scholarly journals Object-Free Definition of Categories

2013 ◽  
Vol 21 (3) ◽  
pp. 193-205
Author(s):  
Marco Riccardi
Keyword(s):  
Binary Relation ◽  
Category Theory ◽  
Final Part ◽  
One To One ◽  
Definition Of

Summary Category theory was formalized in Mizar with two different approaches [7], [18] that correspond to those most commonly used [16], [5]. Since there is a one-to-one correspondence between objects and identity morphisms, some authors have used an approach that does not refer to objects as elements of the theory, and are usually indicated as object-free category [1] or as arrowsonly category [16]. In this article is proposed a new definition of an object-free category, introducing the two properties: left composable and right composable, and a simplification of the notation through a symbol, a binary relation between morphisms, that indicates whether the composition is defined. In the final part we define two functions that allow to switch from the two definitions, with and without objects, and it is shown that their composition produces isomorphic categories.

scholarly journals Fixed Points for a Pair of F-Dominated Contractive Mappings in Rectangular b-Metric Spaces with Graph

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 884 ◽  
Author(s):  
Tahair Rasham ◽  
Giuseppe Marino ◽  
Abdullah Shoaib
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Partial Metric Space ◽  
Contractive Condition ◽  
Partial Metric ◽  
Contractive Mappings ◽  
Dislocated Metric Space ◽  
Definition Of ◽  
Dislocated Metric

Recently, George et al. (in Georgea, R.; Radenovicb, S.; Reshmac, K.P.; Shuklad, S. Rectangular b-metric space and contraction principles. J. Nonlinear Sci. Appl. 2015, 8, 1005–1013) furnished the notion of rectangular b-metric pace (RBMS) by taking the place of the binary sum of triangular inequality in the definition of a b-metric space ternary sum and proved some results for Banach and Kannan contractions in such space. In this paper, we achieved fixed-point results for a pair of F-dominated mappings fulfilling a generalized rational F-dominated contractive condition in the better framework of complete rectangular b-metric spaces complete rectangular b-metric spaces. Some new fixed-point results with graphic contractions for a pair of graph-dominated mappings on rectangular b-metric space have been obtained. Some examples are given to illustrate our conclusions. New results in ordered spaces, partial b-metric space, dislocated metric space, dislocated b-metric space, partial metric space, b-metric space, rectangular metric spaces, and metric space can be obtained as corollaries of our results.

scholarly journals Nilpotent Group C*-algebras as Compact Quantum Metric Spaces

2017 ◽  
Vol 60 (1) ◽  
pp. 77-94 ◽  
Author(s):  
Michael Christ ◽  
Marc A. Rieòel
Keyword(s):  
Finite Groups ◽  
Word Length ◽  
Polynomial Growth ◽  
Metric Spaces ◽  
Length Function ◽  
C Algebra ◽  
Pointwise Multiplication ◽  
C Algebras ◽  
Definition Of ◽  
Compact Quantum Metric Space

AbstractLet be a length function on a group G, and let M denote the operator of pointwise multiplication by on l2(G). Following Connes, M𝕃 can be used as a “Dirac” operator for the reduced group C*-algebra (G). It deûnes a Lipschitz seminorm on (G), which defines a metric on the state space of (G). We show that for any length function satisfying a strong form of polynomial growth on a discrete group, the topology from this metric coincides with the weak-* topology (a key property for the definition of a “compact quantum metric space”). In particular, this holds for all word-length functions on ûnitely generated nilpotent-by-finite groups.

scholarly journals Efficient Parameterized Word Matching Using Bit-Parallelism and Partitioning the Text

2016 ◽  
Vol 2 (2) ◽  
pp. 20
Author(s):  
Rajesh Prasad
Keyword(s):  
Experimental Results ◽  
Brute Force ◽  
White Space ◽  
Matching Problem ◽  
One To One ◽  
Brute Force Approach ◽  
Better Than

Word matching problem is to find all the exact occurrences of a pattern P[0...m-1] in the text T[0...n-1], where P neither contains any white space nor preceded and followed by space. In the parameterized word matching problem, a given word P[0...m-1] is said to match with a sub-word t of the text T[0...n-1], if there exists a one-to-one correspondence between the symbols of P and the symbols of t. Exact Word Matching (EWM) problem has been previously solved by partitioning the text into number of tables in the pre-processing phase and then applying either brute force approach or fast hashing during the searching process. This paper presents an extension of EWM problem for parameterized word matching. It first split the text into number of tables in the pre-processing phase and then applying prev-encoding and bit-parallelism technique, Parameterized Shift-Or (PSO) during the searching phase. Experimental results show that this technique performs better than PSO.

scholarly journals Approximations of Variational Problems in Terms of Variational Convergence

2017 ◽  
Vol 20 (K2) ◽  
pp. 107-116
Author(s):  
Diem Thi Hong Huynh
Keyword(s):  
Multiobjective Optimization ◽  
Metric Space ◽  
Metric Spaces ◽  
Equilibrium Problems ◽  
Variational Problems ◽  
Dimensional Case ◽  
Variational Convergence ◽  
Finite Dimensional ◽  
Finite Dimensional Case ◽  
Definition Of

We show first the definition of variational convergence of unifunctions and their basic variational properties. In the next section, we extend this variational convergence definition in case the functions which are defined on product two sets (bifunctions or bicomponent functions). We present the definition of variational convergence of bifunctions, icluding epi/hypo convergence, minsuplop convergnece and maxinf-lop convergence, defined on metric spaces. Its variational properties are also considered. In this paper, we concern on the properties of epi/hypo convergence to apply these results on optimization proplems in two last sections. Next we move on to the main results that are approximations of typical and important optimization related problems on metric space in terms of the types of variational convergence are equilibrium problems, and multiobjective optimization. When we applied to the finite dimensional case, some of our results improve known one.

scholarly journals Some related fixed point theorems for multivalued mappings on two metric spaces

2020 ◽  
Vol 12 (2) ◽  
pp. 392-400
Author(s):  
Ö. Biçer ◽  
M. Olgun ◽  
T. Alyildiz ◽  
I. Altun
Keyword(s):  
Fixed Point ◽  
Classical Result ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Compact Set ◽  
Complete Metric Spaces ◽  
Bounded Set ◽  
Contraction Type ◽  
Definition Of

The definition of related mappings was introduced by Fisher in 1981. He proved some theorems about the existence of fixed points of single valued mappings defined on two complete metric spaces and relations between these mappings. In this paper, we present some related fixed point results for multivalued mappings on two complete metric spaces. First we give a classical result which is an extension of the main result of Fisher to the multivalued case. Then considering the recent technique of Wardowski, we provide two related fixed point results for both compact set valued and closed bounded set valued mappings via $F$-contraction type conditions.

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