Presses universitaires de Louvain
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<TitleText>Thèses de l'Université catholique de Louvain (UCL)</TitleText>
Numéro 631
Thèses de la Faculté des sciences économiques, sociales, politiques et de communication
631
<TitleType>01</TitleType>
<TitleText>A theory of games with general complementarities</TitleText>
<TitlePrefix>A</TitlePrefix>
<TitleWithoutPrefix>Theory of games with general complementarities</TitleWithoutPrefix>
01
GCOI
29303100197220
1
A01
Filippo L. Calciano
Calciano, Filippo L.
Filippo L.
Calciano
<p>Filippo L. Calciano holds a B.A. in economics from the University of Rome 1 and a M.A. in economics from the University of Pennsylvania. After a visiting period at the London School of Economics, he has been Research Fellow at the Center<br /> for Operations Research and Econometrics.</p>
1
01
eng
80
00
80
03
26
1
BUS000000
29
2012
3283
SCIENCES POLITIQUES
24
INTERNET
Théories économiques
93
JPA
01
06
Économistes
01
<P>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
03
<P>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
02
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.
01
<P>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.</P>
<P>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.</P>
<P>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.</P>
<P>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</P>
<P>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.</P>
<P>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.</p>
03
<P>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.</P>
<P>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.</P>
<P>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.</P>
<P>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</P>
<P>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.</P>
<P>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.</p>
02
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.
04
<p>Acknowledgments i<br />
Preface v<br />
Chapter 1. The Mathematics of Complementarity 1<br />
1. Introduction 1<br />
2. Cardinal and ordinal complementarity 2<br />
3. Cardinal versus ordinal complementarity 6<br />
4. Monotone comparative statics on chains 8<br />
5. Monotone comparative statics on finite products of chains 9<br />
6. Monotone comparative statics on lattices 14<br />
7. Applications to Cournot and Bertrand competition 18<br />
Chapter 2. Fixed Points of Increasing Correspondences 21<br />
1. Introduction 21<br />
2. Background material on lattices 21<br />
3. Increasing correspondences 22<br />
4. Extremal fixpoints and their comparative statics 24<br />
5. Order structure of the fixpoint set 28<br />
Chapter 3. A Theory of Comparative Statics with General Complementarities 33<br />
1. Introduction 33<br />
2. Generalized modularity and generalized increasing differences 35<br />
3. Quasilattices 40<br />
4. Comparative statics of optimal solutions 47<br />
Chapter 4. Games with General Complementarities 53<br />
1. Introduction 53<br />
2. The standard games with strategic complementarities and their properties 53<br />
3. Games with general complementarities and their properties 55<br />
4. Sufficient conditions on payoffs 56<br />
5. Rationalizability 58<br />
6. Application: A Diamond-type search model 60<br />
7. Application: Oligopoly theory 62<br />
References 67</p>
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