Mathematical Foundations of Game Theory by Rida Laraki (English) Paperback Book

Back Cover

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.

Table of Contents

1 Introduction.- 2 Zero-Sum Games: the Finite Case.- 3 Zero-Sum Games: the General Case.- 4 N-Player games: Rationality and Equilibria.- 5 Equilibrium Manifolds and Dynamics.- 6 Games in Extensive Form.- 7 Correlated Equilibria, Learning, Bayesian Equilibria.- 8 Introduction to Repeated Games.- 9 Solutions to the Exercises.- References. 

Review

"The book is a very valuable one and a nice piece of work in the area of game theory. … The book is enjoyable to read and truly an enrichment in game theory. It is widely well-structured and well-written and mathematically correct. … I recommend the book for researchers, graduate and undergraduate students who wants to get some insight in noncooperative game theory." (Sirma Zeynep Alparslan-Gok, zbMATH 1426.91002, 2020)

Review Quote

"The book is a very valuable one and a nice piece of work in the area of game theory. ... The book is enjoyable to read and truly an enrichment in game theory. It is widely well-structured and well-written and mathematically correct. ... I recommend the book for researchers, graduate and undergraduate students who wants to get some insight in noncooperative game theory." (Sirma Zeynep Alparslan-Gok, zbMATH 1426.91002, 2020)

Feature

Provides a self-contained presentation of the mathematical foundations of Game Theory including recent advances in dynamics and learning All results are proved in their full generality using tools and concepts defined in the text Includes 60 exercises, with solutions, which often contain complementary results and alternative proofs

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