Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgment
- Notation
- Part IIntroductory Material
- Part IIGame Solving and Regret Minimization
- 4Regret Minimization and the Minimax Theorem
- 5Blackwell Approachability and Regret Matching
- 6Self-Play via Regret Minimization
- 7Optimism and Fast Convergence of Self-Play
- 8Extensive-Form Games
- 9Stackelberg Equilibrium and Security Games
- 10Fixed-Point Theorems and Equilibrium Existence
- Part IIIFair Allocation and Market Equilibrium
- Part IVAuctions and Internet Advertising Markets
- Appendix AOptimization Background
- Appendix BProbability Background
- References
- Index
10 - Fixed-Point Theorems and Equilibrium Existence
from Part II - Game Solving and Regret Minimization
Published online by Cambridge University Press: 20 August 2026
Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgment
- Notation
- Part IIntroductory Material
- Part IIGame Solving and Regret Minimization
- 4Regret Minimization and the Minimax Theorem
- 5Blackwell Approachability and Regret Matching
- 6Self-Play via Regret Minimization
- 7Optimism and Fast Convergence of Self-Play
- 8Extensive-Form Games
- 9Stackelberg Equilibrium and Security Games
- 10Fixed-Point Theorems and Equilibrium Existence
- Part IIIFair Allocation and Market Equilibrium
- Part IVAuctions and Internet Advertising Markets
- Appendix AOptimization Background
- Appendix BProbability Background
- References
- Index
Summary
This chapter gives an overview of the most important fixed-point theorems for showing the existence of game-theoretic equilibria and market equilibria. In particular, we introduce Brouwer’s fixed-point theorem and Kakutani’s fixed-point theorem, and then we demonstrate how they can be used to prove a variety of existence results.
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- Games, Markets, and Online Learning , pp. 109 - 116Publisher: Cambridge University PressPrint publication year: 2026
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