A Theory of games with general complementarities

Contents

Acknowledgments i
Preface v
Chapter 1. The Mathematics of Complementarity 1
1. Introduction 1
2. Cardinal and ordinal complementarity 2
3. Cardinal versus ordinal complementarity 6
4. Monotone comparative statics on chains 8
5. Monotone comparative statics on finite products of chains 9
6. Monotone comparative statics on lattices 14
7. Applications to Cournot and Bertrand competition 18
Chapter 2. Fixed Points of Increasing Correspondences 21
1. Introduction 21
2. Background material on lattices 21
3. Increasing correspondences 22
4. Extremal fixpoints and their comparative statics 24
5. Order structure of the fixpoint set 28
Chapter 3. A Theory of Comparative Statics with General Complementarities 33
1. Introduction 33
2. Generalized modularity and generalized increasing differences 35
3. Quasilattices 40
4. Comparative statics of optimal solutions 47
Chapter 4. Games with General Complementarities 53
1. Introduction 53
2. The standard games with strategic complementarities and their properties 53
3. Games with general complementarities and their properties 55
4. Sufficient conditions on payoffs 56
5. Rationalizability 58
6. Application: A Diamond-type search model 60
7. Application: Oligopoly theory 62
References 67