A theory of games with general complementarities


Première édition

In the current theory of games, the formal notion of complementarity that is employed is unsatisfactory because it bears too few connections with our intuitive idea of complementarity. This is the starting point of the present work. Lire la suite

The current theory of games with strategic complementarities, also know as supermodular or quasisupermodular games, sets up a fundamental tool to investigate strategic interactions where diffuse Pareto-Edgeworth complementarities among the actions of t


The current theory of games with strategic complementarities, also know as supermodular or quasisupermodular games, sets up a fundamental tool to investigate strategic interactions where diffuse Pareto-Edgeworth complementarities among the actions of the agents are present. It represents the basic analytical framework for modern industrial organization, and finds plenty of applications in strategic macroeconomics and in microeconomics at large.

However, the formal notion of complementarity that is employed in this theory is unsatisfactory because it bears too few connections with our intuitive idea of complementarity. This is the starting point of the present work.

We introduce a notion of complementarity that is more meaningful from an economic point of view, and investigate how far we can go from it. We define a new class of games, that we call games with general complementarities, and obtain for these games results in terms of existence of greatest and least Nash equilibria, comparative statics of these extremal equilibria, lattice structure of the Nash set, and rationalizability of Nash profiles.

Our games with general complementarities retain many of the basic properties of games with strategic complementarities. In the presence of this, our work represents a generalization of the latter class of games

Games with strategic complementarities are a mathematical construction that merges an order-based fixpoint theory, in the vein of Tarski, with an approach to comparative statics for payoffs defined on lattices, independently developed in operations research. To attain our results, we have generalized both the fixpoint part of the theory of games with strategic complementarities and its comparative statics part. These intermediary results have their own independent interest.

We present applications of our games with general complementarities to models of search and models of oligopoly, problems that are not tractable with standard tools.


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Spécifications


Éditeur
Presses universitaires de Louvain
Partie du titre
Numéro 631
Auteur
Filippo L. Calciano,
Collection
Thèses de la Faculté des sciences économiques, sociales, politiques et de communication | n° 631
Langue
anglais
Catégorie (éditeur)
Sciences économiques et sociales > Sciences économiques > Théories économiques
BISAC Subject Heading
BUS000000 BUSINESS & ECONOMICS
Code publique Onix
06 Professionnel et académique
CLIL (Version 2013-2019 )
3283 SCIENCES POLITIQUES
Description public visé
Économistes
Date de première publication du titre
01 septembre 2010
Subject Scheme Identifier Code
Classification thématique Thema: Sciences politiques et théorie
Type d'ouvrage
Thèse
Avec
Bibliographie

Livre broché


Date de publication
10 février 2013
ISBN-13
978-2-87558-119-8
Ampleur
Nombre de pages de contenu principal : 172
Dépôt Légal
D/2013/9964/6 Louvain-la-Neuve, Belgique
Code interne
87757
Format
16 x 24 x 1 cm
Poids
288 grammes
Prix
30,00 €
ONIX XML
Version 2.1, Version 3

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Sommaire


1 Introduction 1
1.1 Motivation . 1
1.2 Overview 8
2 The discontinuous Galerkin method 11
2.1 Model equations11
2.2 Elements and functional spaces . 12
2.3 Variational formulation 14
2.4 Shape functions23
3 Extending the DG variational formulation 27
3.1 Stability of the interior penalty method on hybrid meshes27
3.2 Non-conformal formulation . 35
3.3 Frequential formulation of the homentropic LEE . 44
4 Iterative methods 57
4.1 Newton methods . 59
4.2 Multigrid methods 63
4.3 Concluding remarks . 71
5 Efficient data structures 75
5.1 Algebraic primitives on the computer . 76
5.2 Data Structures84
5.3 Efficient assembly . 89
5.4 Conclusions 102
6 noFUDGe: a first industrial application 105
6.1 Description of the flow 106
6.2 Computational setup . 106
6.3 Comparison of computed flow fields108
6.4 Validation . 114
6.5 Comparison of computational cost. 116
6.6 Scaling tests 116
6.7 Conclusions 118
i
ii CONTENTS
7 Current status and prospects 119
7.1 Conclusions 119
7.2 Current status of the Argo group 120
7.3 Prospects 121
A Elements of functional analysis A.3
A.1 Hilbert spaces. A.3
A.2 Solvability of variational problems. A.4
A.3 The Lax-Milgram theoremA.5
A.4 The most simple exampleA.5
B Function spaces, reference elements and quadrature A.7
B.1 Construction of Lagrange interpolants . A.7
B.2 Interpolation on the boundary A.8
B.3 Specific elements . A.9
B.4 Quadrature rules . A.12
C Sharp values for the trace inverse inequality A.15
C.1 Simplices A.16
C.2 Outline ofWarburton's method . A.16
C.3 Tensor product elements. A.17
C.4 Wedges . A.19
C.5 Lagrange interpolation on pyramidsA.21
C.6 The Pascal space on the pyramid A.25
D Nonlinear instability of quadrature-free methods A.27
D.1 Original formulation . A.27
D.2 Extension to non-linear equations of state . A.30
D.3 Spurious modesA.30
Bibliography i