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Mathematical Foundations of Game Theory

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Date
2019
Publisher city
Cham
Publisher
Springer
Publishing date
2019
ISBN:
978-3-030-26645-5
Collection title
Universitext book series (UTX)
Dewey
Probabilités et mathématiques appliquées
Sujet
zero-sum games; minmax theorem; Nash equilibrium; rationalizability; normal form games
URI
https://basepub.dauphine.fr/handle/123456789/19919
Collections
  • LAMSADE : Publications
Metadata
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Author
Laraki, Rida
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Renault, Jérôme
115536 autre
Sorin, Sylvain
542596 Institut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]
Type
Ouvrage
Abstract (EN)
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.

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