Advertisement

Mathematical Foundations of Game Theory

  • Rida Laraki
  • Jérôme Renault
  • Sylvain Sorin
Textbook

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Rida Laraki, Jérôme Renault, Sylvain Sorin
    Pages 1-12
  3. Rida Laraki, Jérôme Renault, Sylvain Sorin
    Pages 13-31
  4. Rida Laraki, Jérôme Renault, Sylvain Sorin
    Pages 33-44
  5. Rida Laraki, Jérôme Renault, Sylvain Sorin
    Pages 45-75
  6. Rida Laraki, Jérôme Renault, Sylvain Sorin
    Pages 77-95
  7. Rida Laraki, Jérôme Renault, Sylvain Sorin
    Pages 97-128
  8. Rida Laraki, Jérôme Renault, Sylvain Sorin
    Pages 129-149
  9. Rida Laraki, Jérôme Renault, Sylvain Sorin
    Pages 151-181
  10. Rida Laraki, Jérôme Renault, Sylvain Sorin
    Pages 183-213
  11. Back Matter
    Pages 215-229

About this book

Introduction

This book gives a concise presentation of the mathematical foundations of Game Theory, with an emphasis on strategic analysis linked to information and dynamics. It is largely self-contained, with all of the key tools and concepts defined in the text.

Combining the basics of Game Theory, such as value existence theorems in zero-sum games and equilibrium existence theorems for non-zero-sum games, with a selection of important and more recent topics such as the equilibrium manifold and learning dynamics, the book quickly takes the reader close to the state of the art. Applications to economics, biology, and learning are included, and the exercises, which often contain noteworthy results, provide an important complement to the text. 

Based on lectures given in Paris over several years, this textbook will be useful for rigorous, up-to-date courses on the subject. Apart from an interest in strategic thinking and a taste for mathematical formalism, the only prerequisite for reading the book is a solid knowledge of mathematics at the undergraduate level, including basic analysis, linear algebra, and probability. 

Keywords

zero-sum games minmax theorem Nash equilibrium rationalizability normal form games extensive form games discontinuous games perfect recall sequential equilibrium equilibrium manifold replicator dynamics external regret internal regret repeated games

Authors and affiliations

  • Rida Laraki
    • 1
  • Jérôme Renault
    • 2
  • Sylvain Sorin
    • 3
  1. 1.CNRSLamsade Université de Paris Dauphine-PSLParisFrance
  2. 2.Toulouse School of EconomicsUniversité Toulouse 1 CapitoleToulouseFrance
  3. 3.Institut de Mathématiques de Jussieu-PRGSorbonne UniversitéParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-26646-2
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-26645-5
  • Online ISBN 978-3-030-26646-2
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site
Industry Sectors
Pharma
Chemical Manufacturing
Finance, Business & Banking