The thesis consists of five chapters. The first of them contains introduction. Chapter 2 considers a broad class of two player symmetric games, which display a fundamental non-concavity when actions of both players are about to be the same. This impl
1 INTRODUCTION 1
1.1 Problem: heterogeneity . . . . . . . . . . . . . . . . 1
1.2 Methodology: complementarity . . . . . . . . . . . 3
1.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 ENDOGENOUS HETEROGENEITY IN STRATEGICMODELS: SYMMETRY BREAKING VIA STRATEGIC SUBSTITUTES AND NON-CONCAVITIES 11
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3 Endogenous heterogeneity with strategic substitutes 22
2.3.1 The results . . . . . . . . . . . . . . . . . . 24
2.3.2 Applications . . . . . . . . . . . . . . . . . . 28
2.3.2.1 R&D investment . . . . . . . . . . 28
2.3.2.2 Provision of information . . . . . . 32
2.4 Endogenous heterogeneity without monotonic best replies . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.4.1 The results . . . . . . . . . . . . . . . . . . 36
2.4.2 Applications: quality investment . . . . . . . 41
2.5 Convex Payo¤s . . . . . . . . . . . . . . . . . . . . 43
2.5.1 Applications . . . . . . . . . . . . . . . . . . 45
2.6 Extensions . . . . . . . . . . . . . . . . . . . . . . . 46
i
2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . 48
2.8 Appendix . . . . . . . . . . . . . . . . . . . . . . . 50
2.8.1 Summary of supermodular/submodular games 50
2.8.2 Proofs of Section 2.3 . . . . . . . . . . . . . 52
2.8.3 Proofs of Section 2.4 . . . . . . . . . . . . . 61
2.8.4 Proofs of Section 2.6 . . . . . . . . . . . . . 63
3 SYMMETRIC VERSUS ASYMMETRIC EQUILIBRIA IN SYMMETRIC N PLAYER SUPERMODULAR GAMES 71
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 71
3.2 Lattice-theoretic preliminaries . . . . . . . . . . . . 75
3.3 Symmetric versus asymmetric PSNE . . . . . . . . 78
3.4 On the scope of our results . . . . . . . . . . . . . . 91
3.4.1 Submodular games . . . . . . . . . . . . . . 92
3.4.2 Games with quasi-convex payo¤s . . . . . . 94
4 MARKET TRANSPARENCY AND BERTRAND COMPETITION 101
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 101
4.2 Setup and de.nitions . . . . . . . . . . . . . . . . . 105
4.2.1 General setup . . . . . . . . . . . . . . 105
4.2.2 Useful de.nitions and results . . . . . . . . . 107
4.3 E¤ect of transparency on prices . . . . . . . . . . . 109
4.3.1 Strategic complementarities . . . . . . . . . 109
4.3.2 Strategic substitutes . . . . . . . . . . . . . 112
4.3.2.1 Symmetric games . . . . . . . . . . 113
4.3.2.2 Asymmetric games . . . . . . . . . 114
4.4 E¤ects of transparency on pro.ts . . . . . . . . . . 117
4.5 Linear example . . . . . . . . . . . . . . . . . . . . 119
4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . 122
5 STRATEGIC SUBSTITUTES AND COMPLEMENTS IN COURNOT OLIGOPOLYWITH PRODUCT DIFFERENTIATION 127
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 127
5.2 Supermodular games . . . . . . . . . . . . . . . . . 129
5.3 Conditions and examples . . . . . . . . . . . . . . . 133
5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . 142
5.5 Appendix . . . . . . . . . . . . . . . . . . . . . . . 143