Monotone Games: A Unified Approach to Games with Strategic Complements and Substitutes 9783030455125
This Palgrave Pivot examines monotone games and studies incentives and outcomes when there are multiple players, and how
259 98 2MB
English Pages 166 [176] Year 2020
Table of contents :
Preface
Contents
List of Figures
List of Tables
1 Introduction
2 Elements of Lattice Games
2.1 Lattices
2.1.1 Partially Ordered Set
2.1.2 Join and Meet
2.1.3 Lattice
2.1.4 Interval
2.1.5 Complete Lattice
2.1.6 Lattice Set Order
2.1.7 Correspondence and Fixed Point
2.2 Lattice Game
2.2.1 Definition
2.2.2 Best Response
2.2.3 Nash Equilibrium Set
2.2.4 Dominance Solvability and Global Stability
2.2.5 Parameterized Lattice Games
References
3 Games with Strategic Complements
3.1 Codirectional Incentives
3.1.1 Increasing Differences
3.1.2 Supermodular Function
3.1.3 Single Crossing Property
3.1.4 Quasisupermodular Function
3.1.5 Increasing Maximizers
3.2 Game with Strategic Complements
3.2.1 Definition
3.2.2 Increasing Best Response
3.2.3 Nash Equilibrium Set
3.2.4 Dominance Solvability and Global Stability
3.2.5 Monotone Comparative Statics of Equilibrium
References
4 Games with Strategic Substitutes
4.1 Contradirectional Incentives
4.1.1 Decreasing Differences
4.1.2 Submodular Function
4.1.3 Dual Single Crossing Property
4.1.4 Quasisubmodular Function
4.1.5 Decreasing Maximizers
4.2 Game with Strategic Substitutes
4.2.1 Definition
4.2.2 Decreasing Best Response
4.2.3 Nash Equilibrium Set
4.2.4 Dominance Solvability and Global Stability
4.2.5 Monotone Comparative Statics of Equilibrium
References
5 Monotone Games
5.1 Monotone Incentives
5.2 Monotone Game
5.2.1 Definition
5.2.2 Monotone Best Response
5.2.3 Nash Equilibrium Set
5.2.4 Dominance Solvability and Global Stability
5.2.5 Monotone Comparative Statics of Equilibrium
References
Index
Preface
Contents
List of Figures
List of Tables
1 Introduction
2 Elements of Lattice Games
2.1 Lattices
2.1.1 Partially Ordered Set
2.1.2 Join and Meet
2.1.3 Lattice
2.1.4 Interval
2.1.5 Complete Lattice
2.1.6 Lattice Set Order
2.1.7 Correspondence and Fixed Point
2.2 Lattice Game
2.2.1 Definition
2.2.2 Best Response
2.2.3 Nash Equilibrium Set
2.2.4 Dominance Solvability and Global Stability
2.2.5 Parameterized Lattice Games
References
3 Games with Strategic Complements
3.1 Codirectional Incentives
3.1.1 Increasing Differences
3.1.2 Supermodular Function
3.1.3 Single Crossing Property
3.1.4 Quasisupermodular Function
3.1.5 Increasing Maximizers
3.2 Game with Strategic Complements
3.2.1 Definition
3.2.2 Increasing Best Response
3.2.3 Nash Equilibrium Set
3.2.4 Dominance Solvability and Global Stability
3.2.5 Monotone Comparative Statics of Equilibrium
References
4 Games with Strategic Substitutes
4.1 Contradirectional Incentives
4.1.1 Decreasing Differences
4.1.2 Submodular Function
4.1.3 Dual Single Crossing Property
4.1.4 Quasisubmodular Function
4.1.5 Decreasing Maximizers
4.2 Game with Strategic Substitutes
4.2.1 Definition
4.2.2 Decreasing Best Response
4.2.3 Nash Equilibrium Set
4.2.4 Dominance Solvability and Global Stability
4.2.5 Monotone Comparative Statics of Equilibrium
References
5 Monotone Games
5.1 Monotone Incentives
5.2 Monotone Game
5.2.1 Definition
5.2.2 Monotone Best Response
5.2.3 Nash Equilibrium Set
5.2.4 Dominance Solvability and Global Stability
5.2.5 Monotone Comparative Statics of Equilibrium
References
Index
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